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Innovative Reactive Energy Management for a Photovoltaic Battery System
Available online at www.sciencedirect.com
ScienceDirect Energy Procedia 99 (2016) 341 – 349
10th International Renewable Energy Storage Conference, IRES 2016, 15-17 March 2016, Düsseldorf, Germany
Innovative Reactive Energy Management for a Photovoltaic Battery System Michael Böttiger*, Martin Paulitschke, Thilo Bocklisch Technische Universität Dresden, chair of Energy Storage Systems, George-Baehr-Str 3c, 01069 Dresden, Germany
Abstract This paper presents an optimizing model-based energy management system for an AC-coupled grid connected photovoltaic battery system. The energy management consists of a prediction module, an optimization module, and a reactive management module. The main focus of this article is to present an innovative reactive management that can handle forecast uncertainties. The so called “SOC-bound method” will be described in detail. Main idea is to combine the outputs of the dynamic programming algorithm with a simple rule-based strategy. Furthermore, the results of a start-time and start-/end-SOC sensitivity analysis concerning the six performance criteria self-sufficiency, self-consumption, grid relief factor, economic parameter, battery full cycles, and specific battery stress value will be discussed. © 2016 2016 The byby Elsevier Ltd.Ltd. This is an open access article under the CC BY-NC-ND license Authors.Published Published Elsevier © TheAuthors. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of EUROSOLAR - The European Association for Renewable Energy. Peer-review under responsibility of EUROSOLAR - The European Association for Renewable Energy
Keywords: energy management, dynamic programming, energy storage, power flow optimization, smart home
1.
Introduction
Many international studies present energy management (EM) concepts for grid connected photovoltaic (PV) battery systems in residential buildings [1 – 14]. These can be classified in rule-based and optimization-based concepts. Simple rule-based approaches [1, 2], mostly found in commercial PV battery systems, only maximize the self-consumption of solar energy (one optimization criterion) as follows: If there is more PV power available than the consumer demand and the battery is not fully charged, the energy is stored. If the consumption is higher than the
* Corresponding author. Tel.: +49-351-463-40268; fax: +49-351-463-40270. E-mail address: [email protected]
1876-6102 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of EUROSOLAR - The European Association for Renewable Energy doi:10.1016/j.egypro.2016.10.124
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PV power, the load is supplied by the battery. A major disadvantage is a fully charged battery before reaching the midday peak. The consequences are a high feed-in power or curtailment losses. To overcome this problem improved rule-based concepts additionally relieves the grid by reducing the maximum feed-in power (two optimization criteria) and obtains a fully charged battery in the evening [3 – 6]. Considering further criteria such as battery lifetime, variable price and feed-in tariffs and component losses over time, optimization-based concepts are utilized. Recently, dynamic programming has been applied to solve such multicriteria optimization problems to find an optimal power flow distribution [7 – 13]. Common implementations of an EM with dynamic programming define the optimization start-time at midnight with a start-SOC of 50 % and a prediction horizon of 24 h [7 – 9]. Furthermore, many publications assume ideal PV and load profiles and neglect the influence prediction errors [9 – 13]. One weakness of EM based on dynamic programming is that the quality of the optimization results strongly depends on the prediction accuracy of PV and load profiles. In order to overcome the mentioned prediction uncertainty problem a new “SOC-bound method” will be introduced in this article. Our previous publications [14, 15] presented a model-based EM in detail with subject to the optimization-module and the implementation of the dynamic programming algorithm in the simulation environment Matlab. The structure of this paper is organized as follows: Section 2 describes the system configuration. Section 3 presents the optimizing model-based EM focussing on the SOC-bound method. Section 4 shows and discusses the results of two investigations. First, the influence of the optimization start-time and the start-/end-SOC will be examined. Second, the influence of the SOC-bound will be analyzed. Both investigations are assessed relating to six performance criteria. Section 5 gives a summary and a brief outlook for future research. 2.
System configuration
The AC-coupled PV battery system studied in this paper is shown in Fig. 1. The main components of the system are the PV-generator, the lithium-ion battery, the inverters, the consumer load, the interface to the grid, and the EM. PV-generator
grid
DC/AC - inverter PGrid >0
PPV >0 PLoad >0
PGrid <0 load
AC/DC - inverter EM
PBatt >0
PBatt <0 lithium-ion battery
Fig. 1. Configuration of the AC-coupled PV battery system including the powerflow direction and sign convention.
The PV power PPV is expected to be always positive. The battery power PBatt is assumed to be negative during discharging and positive during charging. The load power PLoad is always positive. The grid power PGrid is negative, if the grid supplies the loads, and positve if power is fed into the grid. The power balance criteria in the AC-coupled system must be valid every time. PPV PLoad PBatt PGrid
0
(1)
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A battery model based on an electric circuit approach was chosen to describe the behavior of the lithium-ion battery [16, 17]. The model consists of a voltage source, a serial resistance, two RC-pairs, and a parallel resistance. The voltage source describes the non-linear relationship between the open-circuit-voltage and the SOC. The serial resistance represents the ohmic losses of the battery. The two series connected RC-pairs characterize the transient behaviour during charge and discharge process. All elements of the electric circuit depend on the SOC and the current direction. Temperature and aging effects are not taken into account in this modelling approach. A simple method, called “Coulomb counting”, was employed to determine the SOC as a function of the battery current. The models of the inverters have been developed using efficiency curves. PV and load behavior were not explicitly modelled in this study. Historical time series relating to PV and load power form the basis for the simulation. Consequently the loads are not controllable and a demand side management isn’t implemented. Optimizinig model-based EMLooking at a typical power profile in a residential building with a PV system there are periods with surplus energy which has to be fed into the grid and periods with energy deficit which has to be supplied by the grid. By adding a lithium-ion battery to such a PV system it depends on the charging strategy of the EM how to use the degree of freedom for storing surplus energy. Furthermore, the EM is responsible for monitoring the system states, forecast PV and load profiles, to optimize the battery charge strategy, and to control the power flows. Based on [14] an optimizing model-based EM (s. Fig. 2) has been implemented.
Prediction module
PPV, pred PLoad, pred
Optimization module
PBatt, pred SOCBatt, pred
Reactive management module
PBatt
measured data PPV , PLoad
k EGP k FIT SOCBatt
PPV, pred PLoad, pred
PPV PLoad
PV battery system
Fig. 2. Structure of the optimizing model-based EM.
It can be divided in a prediction module, an optimization module, and a reactive management module. The prediction module provides a PV and a load profile. In a first step, a simple persistence approach based on historical data was implemented. With the measured PV power from the previous day, the prediction for the next day was built averaged over 15 min. Generating the load forecast follows the same principle. The only difference is that the identical weekday was taken for the prediction of the next day. With the predicted PV and load power the optimization module generates a SOC-trajectory for the next day considering the objectives “electricity costs”, “grid relief”, and “increased battery lifetime”. The mathematical formulation of the objectives is summarized in a cost-function ij. ij
KW K B K PN
(2)
KW presents the criterion for the electricity costs including energy tariffs kEGP and feed-in tariffs kFIT. KPN corresponds to the criterion for grid relief. If the feed-in power PGrid is higher than the limitation PGrid, max, KPN rises
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as a linear function with the feed-in power. The third criterion KB considers battery aging effects. First the number of full cycles will be interpreted as costs. Second, the SOC dwell-time will also be associated with costs. Beginning at a SOC of 50 % with 0 € the costs rise linear to the SOC limits (SOCBatt, min and SOCBatt, max results 0.01 €/SOC-step). The objective function J has to be minimized over the time horizon T of the optimization. T
min J
¦ ij SOC,k
(3)
k 1
The constraints of the problem can be derived from the physical limitations of the lithium-ion battery. To ensure a safe battery operation the SOC and the power PBatt are limited as follows.
SOCBatt,min d SOCBatt d SOCBatt,max
(4)
PBatt, min d PBatt d PBatt, max
(5)
The formulated optimization problem is solved using dynamic programming. Referring to the principle of optimality proposed by Bellman in [16], the optimization problem was divided into sub-problems. Each sub-problem (find the lowest transition costs ij from SOCk to SOCk+1) was solved and then merged to formulate a total solution. Therefore, all possible charge trajectories from the initial SOC at the start of the day to the allowed lithium-ion battery states at the end of the day are evaluated. The SOC-trajectory with the smallest objective function value J presents the optimal battery charge strategy. This resulting strategy matches the optimum for the input data (PPV, pred, PLoad, pred) depending on the defined objectives, restrictions and discretization-steps. The quality of the optimization results generated with dynamic programming strongly depends on the prediction accuracy of the input data (PPV, PLoad). The correction of the optimization results due to bad predictions is the task of the reactive management module. The main idea is to accept power deviations PDev between the prediction values (PPV, pred, PLoad, pred) and the real values (PPV, PLoad) up to a certain limit.
PDev
PPV, pred PLoad, pred PPV PLoad
(6)
The integral of this power deviation PDev is approximately equivalent to a delta SOC. ǻSOCBatt
³ PDev dt
(7)
Based on the SOC-trajectory generated in the optimization module with the dynamic programming algorithm a SOC-bound r'SOC was build. Within the lower and upper bounds, the control of the lithium-ion battery follows the simple strategy that complies with the following two rules. If there is an energy surplus the lithium-ion battery will be charged. When energy is needed, the lithium-ion battery will be discharged. In this case the battery power PBatt is: PBatt
PPV PLoad
(8)
If the SOC reaches one of the bounds, the battery power PBatt is equal to ouput of the optimization module PBatt, The optimal range of the SOC-bounds will be analyzed in the following section. Fig. 3 illustrates a two day sample with a SOC-bound of 5 %. The graph on the top shows the power profile and the lower figure illustrates the SOC-bounds (grey) and the “actual” SOC (blue). pred.
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5000
PP V - PLoad
PGrid
PBatt
power in W
4000 3000 2000 1000 0
-1000 -2000
SOC in %
-3000 bounds
80 60 40 20
SOC
0
5
10
15
20
25 t in h
30
35
40
45
50
Fig. 3. Results of a two day sample with the SOC-bound method.
During night and morning hours the predicted SOC is similar following the simple rule-based strategy. About 9:00 am the sum of the difference between the prediction data and the real data is too high. Consequently the SOC reaches the upper bound. Now the SOC has to follow the upper SOC-bound to guarantee a time delayed charge of the lithium-ion battery. Despite of prediction errors the battery is fully charged before sunset without wasting energy through curtailment. During evening and night hours the lithium-ion battery supplies the electric energy demand. It’s conspicuous that the SOC tends within the SOC-bounds. In this example the optimization was carried at midnight (jump of the SOC-bounds due to new start-SOC of the optimization). The second day follows the same principle. 3.
Simulation results
The simulation input data for the PV and load profiles (four person household) are measured data from a reference object near Chemnitz. The dataset of the studied AC-coupled system introduced in section 2 is given in Tab. 1 including the physical limits and characteristic values which are necessary for dynamic programming. The adjustable parameters SOC-bound, optimization start-time and start-/end-SOC are determined in the respective subsection. Table 1. System parameters and assumptions. System specification
Simulation configuration
PV energy EPV
5000 kWh
Duration tSim
1 year
Electricity consumption ELoad
4000 kWh
Simulation time step tTimestep
1 min
Battery energy EBatt
5 kWh
Prediction horizon TPred
24 h
State of charge SOCBatt
0 % – 100 %
Optimization time step TOpt
15 min
Max. feed in power PGrid_max
2500 W
SOC discretization DSOC
0.005
Energy tariff KEGP
0.30 €/kWh
Feed in tariff KFIT
0.10 €/kWh
In order to evaluate the investigation results six performance criteria have been defined (14 – 19). Equations (9 – 13)
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introduce the basic energy-values PV energy EPV, electricity consumption ELoad, energy fed into the grid EGrid, f, energy consumed by the grid EGrid, c, and the curtailemnt losses ECurt. Table 2. Definition of Energy-values and performance criteria for PV battery system operation. Name
Equation
PV energy EPV
ܧ ൌ න ܲ ሺݐሻ݀ݐ
Electricity consumption ELoad
ܧௗ ൌ නȁܲௗ ȁ݀ݐ
(10)
Energy fed into the grid EGrid, f
ீܧௗǡ ൌ නȁ ሺܲீௗ ሺݐሻǡ Ͳሻȁ݀ݐ
(11)
Energy consumed from the grid EGrid, c
ீܧௗǡ ൌ නȁ ሺܲீௗ ሺݐሻǡ Ͳሻȁ݀ݐ
(12)
Curtailment losses ECurt
ܧ௨௧ ൌ නห ሺܲீௗ ሺݐሻ െ ܲீௗǡ ௫ ሺݐሻǡͲሻห݀ݐ
(13)
ܧௗ െ ீܧௗǡ ݇ௌௌ ൌ ܧௗ ܧ െ ܧ௨௧ െ ீܧௗǡ ݇ௌ ൌ ͳͲͲΨ ή ܧ ܧ௨௧ ݇ோ ൌ ͳͲͲΨ ή ܧ
(14)
Economic parameter kEc
݇ா ൌ ீܧௗǡ ή ܭாீ ீܧௗǡ ή ܭிூ்
(17)
Battery full cycles kBatt, fc
݇௧௧ǡ ൌ
Specific battery stress value kBatt, s
݇௧௧ǡ௦ ൌ ͳͲͲΨ ή නሺܱܵܥ௧௧ ͻͲΨሻ݀ݐ
Self-sufficiency kSS Self-consumption kSC Grid relief factor kR
(9)
(15) (16)
ȁܲ௧௧ ȁ݀ݐ ܧ௧௧
(18) (19)
Fig. 4 illustrates the results of the optimization start-time and start-/end-SOC sensitivity analysis related to the six performance criteria performed with the persistence-forecast. The start-/end-SOC varies between 0 % and 100 %. The start-time TStart of the optimization varies between 0 and 24 o’clock. The prediction horizon TPred was set to 24 h. The best value shows the green cross and the worst value shows the red cross. Self-sufficiency k SS
0
8 12
+ 30
20 28 0
(d)
20
40 60 SOCBatt in %
80
+
+
20
+
+
380
20 20
40 60 SOCBatt in %
80
100
time of day in h
8 12
0
20
40 60 SOCBatt in %
80
16
+
+
+
180
12 16
+ 0
20
40 60 SOCBatt in %
80
0
20
40 60 SOCBatt in %
80
100
(f) Specific battery stress value k Batt, s 0
4 8
24
8 12
24
100
Battery full cycles k Batt, fc
20
4
20
200
time of day in h
12
26
0
4
24 0
34
(e)
0
16
8
24
100
Economic parameter k Ec
32
Grid relief factor k R 0
30
4
16
(c)
time of day in h
16
time of day in h
time of day in h
+
4
24
Self-consumption k SC
(b)
0
time of day in h
(a)
100
4 8
+
12
+
16 20 24
0
20
40 60 SOCBatt in %
80
100
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Fig. 4. Results of the optimization start-time and start-/end-SOC sensitivity analysis. The green cross shows the best value and the red cross shows the worst value.
45
+
40 35 30 25
0
400
20 40 60 80 100 SOC-bound in % (d)
350 300
+
250 200 150
0
20 40 60 80 SOC-bound in %
100
65
(b)
60 55
+
50 45 40
0
300
20 40 60 80 100 SOC-bound in % (e)
260
+
220 180 140 100
0
20 40 60 80 100 SOC-bound in %
Grid relief factor k R in %
(a)
7.5
(c)
7.25 7 6.75 6.5 6.25
Spec. battery stress value k Batt, s
Self-consumption k SC in %
50
Battery full cycles k Batt, fc
Economic parameter k Ec in €
Self-sufficiency k SS in %
The highest self-sufficiency rate in Fig. 4(a) and the highest self-consumption rate in Fig 4(b) can be reached with an optimization start-time at 1:00 pm and a SOC of 80 % – 90 %. The best relief factor in Fig. 4(c) can also be found at a high SOC during midday. An unfavourable grid relief factor results starting the optimization at 4:00 pm with a SOC about 5 %. Looking at the electricity cost in Fig. 4(d) the best values can be found at 2:00 pm with a SOC of 90 %. Fig. 4(e) illustrates that the battery full cycles are nearly independent of the optimization start-time. The lowest number of battery cycles is reached for a SOC of 45 %. Fig. 4(f) shows the specific battery stress factor. Here, the best value can be obtained by starting the optimization at 3:00 pm with a SOC of 10 %. Noticeable is the steep rise of the values with a SOC of 80 %. Considering all six performance criteria it can be said that an optimization start-time in the evening at 5:00 pm with a start-SOC of 80 % produces the best results. The second investigation illustrates the results concerning the sensitivity analysis of the SOC-bounds (0 % – 100 %). A SOC-bound of 100 % corresponds to the rule-based strategy described in section 2. A SOC-bound of 0 % means that the SOC-trajectory generated by the dynamic programming algorithm must be maintained. An investigation of the prediction horizon has shown that the results of the six performance criteria rises with an increasing prediction horizon. Based on this investigation the prediction horizon TPred is set to 30 h and the daily optimization starts at 5:00 pm. Fig. 5 illustrates the simulation results for each performance criterion.
+ 0
25
20 40 60 80 100 SOC-bound in % (f)
20 15 10 5 0
+ 0
20 40 60 80 100 SOC-bound in %
Fig. 5. Results of the SOC-bound variation.
It's evident that a SOC-bound of 0 % isn't a good choice. The electricity costs are too high, self-consumption and self-sufficiency are not acceptable. The red point at a SOC-bound of 20 % leads to a compromise between the battery aging criteria (Fig. 5(e) and Fig. 5(f)) and the electricity cost Fig. 5(d). With this adjustment the battery full cycles are not higher than for the rule-based strategy. Furthermore, the electricity costs are about 50 € higher, but the battery aging will be slowed down by avoiding disadvantageous SOC's.
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4.
Conclusion
The paper has presented an optimizing model-based EM for a PV battery system consisting of a prediction module, an optimization module, and a reactive management module. Highlighted in this paper was the innovative reactive energy management. Simulation results show the sensitivity of the start/end-SOC and the optimization starttime towards the six defined performance criteria. Additionally, a sensitivity analysis of the SOC-bounds shows for a tolerance-band of 20 % good results related to electricity costs, battery lifetime, and curtailment losses. Currently, adaptive optimization techniques including further optimization criteria are investigated. In ongoing research projects the EM will be tested and benchmarked with other management strategies. Moreover, the EM will be integrated in the intelligent sizing algorithm employing particle-swarm-optimization [19, 20]. References [1] [2]
[3] [4] [5]
[6]
[7] [8]
[9] [10] [11] [12] [13]
[14] [15] [16]
[17]
[18] [19]
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Michael Böttiger et al. / Energy Procedia 99 (2016) 341 – 349 [20] Paulitschke M, Bocklisch T, Böttiger M, “Sizing algorithm for a PV-battery-H2-hybrid system employing particle swarm optimization”, Energy Procedia, vol. 73, (2015), DOI: 10.1016/j.egypro.2015.07.664.
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ScienceDirect Energy Procedia 99 (2016) 341 – 349
10th International Renewable Energy Storage Conference, IRES 2016, 15-17 March 2016, Düsseldorf, Germany
Innovative Reactive Energy Management for a Photovoltaic Battery System Michael Böttiger*, Martin Paulitschke, Thilo Bocklisch Technische Universität Dresden, chair of Energy Storage Systems, George-Baehr-Str 3c, 01069 Dresden, Germany
Abstract This paper presents an optimizing model-based energy management system for an AC-coupled grid connected photovoltaic battery system. The energy management consists of a prediction module, an optimization module, and a reactive management module. The main focus of this article is to present an innovative reactive management that can handle forecast uncertainties. The so called “SOC-bound method” will be described in detail. Main idea is to combine the outputs of the dynamic programming algorithm with a simple rule-based strategy. Furthermore, the results of a start-time and start-/end-SOC sensitivity analysis concerning the six performance criteria self-sufficiency, self-consumption, grid relief factor, economic parameter, battery full cycles, and specific battery stress value will be discussed. © 2016 2016 The byby Elsevier Ltd.Ltd. This is an open access article under the CC BY-NC-ND license Authors.Published Published Elsevier © TheAuthors. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of EUROSOLAR - The European Association for Renewable Energy. Peer-review under responsibility of EUROSOLAR - The European Association for Renewable Energy
Keywords: energy management, dynamic programming, energy storage, power flow optimization, smart home
1.
Introduction
Many international studies present energy management (EM) concepts for grid connected photovoltaic (PV) battery systems in residential buildings [1 – 14]. These can be classified in rule-based and optimization-based concepts. Simple rule-based approaches [1, 2], mostly found in commercial PV battery systems, only maximize the self-consumption of solar energy (one optimization criterion) as follows: If there is more PV power available than the consumer demand and the battery is not fully charged, the energy is stored. If the consumption is higher than the
* Corresponding author. Tel.: +49-351-463-40268; fax: +49-351-463-40270. E-mail address: [email protected]
1876-6102 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of EUROSOLAR - The European Association for Renewable Energy doi:10.1016/j.egypro.2016.10.124
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PV power, the load is supplied by the battery. A major disadvantage is a fully charged battery before reaching the midday peak. The consequences are a high feed-in power or curtailment losses. To overcome this problem improved rule-based concepts additionally relieves the grid by reducing the maximum feed-in power (two optimization criteria) and obtains a fully charged battery in the evening [3 – 6]. Considering further criteria such as battery lifetime, variable price and feed-in tariffs and component losses over time, optimization-based concepts are utilized. Recently, dynamic programming has been applied to solve such multicriteria optimization problems to find an optimal power flow distribution [7 – 13]. Common implementations of an EM with dynamic programming define the optimization start-time at midnight with a start-SOC of 50 % and a prediction horizon of 24 h [7 – 9]. Furthermore, many publications assume ideal PV and load profiles and neglect the influence prediction errors [9 – 13]. One weakness of EM based on dynamic programming is that the quality of the optimization results strongly depends on the prediction accuracy of PV and load profiles. In order to overcome the mentioned prediction uncertainty problem a new “SOC-bound method” will be introduced in this article. Our previous publications [14, 15] presented a model-based EM in detail with subject to the optimization-module and the implementation of the dynamic programming algorithm in the simulation environment Matlab. The structure of this paper is organized as follows: Section 2 describes the system configuration. Section 3 presents the optimizing model-based EM focussing on the SOC-bound method. Section 4 shows and discusses the results of two investigations. First, the influence of the optimization start-time and the start-/end-SOC will be examined. Second, the influence of the SOC-bound will be analyzed. Both investigations are assessed relating to six performance criteria. Section 5 gives a summary and a brief outlook for future research. 2.
System configuration
The AC-coupled PV battery system studied in this paper is shown in Fig. 1. The main components of the system are the PV-generator, the lithium-ion battery, the inverters, the consumer load, the interface to the grid, and the EM. PV-generator
grid
DC/AC - inverter PGrid >0
PPV >0 PLoad >0
PGrid <0 load
AC/DC - inverter EM
PBatt >0
PBatt <0 lithium-ion battery
Fig. 1. Configuration of the AC-coupled PV battery system including the powerflow direction and sign convention.
The PV power PPV is expected to be always positive. The battery power PBatt is assumed to be negative during discharging and positive during charging. The load power PLoad is always positive. The grid power PGrid is negative, if the grid supplies the loads, and positve if power is fed into the grid. The power balance criteria in the AC-coupled system must be valid every time. PPV PLoad PBatt PGrid
0
(1)
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A battery model based on an electric circuit approach was chosen to describe the behavior of the lithium-ion battery [16, 17]. The model consists of a voltage source, a serial resistance, two RC-pairs, and a parallel resistance. The voltage source describes the non-linear relationship between the open-circuit-voltage and the SOC. The serial resistance represents the ohmic losses of the battery. The two series connected RC-pairs characterize the transient behaviour during charge and discharge process. All elements of the electric circuit depend on the SOC and the current direction. Temperature and aging effects are not taken into account in this modelling approach. A simple method, called “Coulomb counting”, was employed to determine the SOC as a function of the battery current. The models of the inverters have been developed using efficiency curves. PV and load behavior were not explicitly modelled in this study. Historical time series relating to PV and load power form the basis for the simulation. Consequently the loads are not controllable and a demand side management isn’t implemented. Optimizinig model-based EMLooking at a typical power profile in a residential building with a PV system there are periods with surplus energy which has to be fed into the grid and periods with energy deficit which has to be supplied by the grid. By adding a lithium-ion battery to such a PV system it depends on the charging strategy of the EM how to use the degree of freedom for storing surplus energy. Furthermore, the EM is responsible for monitoring the system states, forecast PV and load profiles, to optimize the battery charge strategy, and to control the power flows. Based on [14] an optimizing model-based EM (s. Fig. 2) has been implemented.
Prediction module
PPV, pred PLoad, pred
Optimization module
PBatt, pred SOCBatt, pred
Reactive management module
PBatt
measured data PPV , PLoad
k EGP k FIT SOCBatt
PPV, pred PLoad, pred
PPV PLoad
PV battery system
Fig. 2. Structure of the optimizing model-based EM.
It can be divided in a prediction module, an optimization module, and a reactive management module. The prediction module provides a PV and a load profile. In a first step, a simple persistence approach based on historical data was implemented. With the measured PV power from the previous day, the prediction for the next day was built averaged over 15 min. Generating the load forecast follows the same principle. The only difference is that the identical weekday was taken for the prediction of the next day. With the predicted PV and load power the optimization module generates a SOC-trajectory for the next day considering the objectives “electricity costs”, “grid relief”, and “increased battery lifetime”. The mathematical formulation of the objectives is summarized in a cost-function ij. ij
KW K B K PN
(2)
KW presents the criterion for the electricity costs including energy tariffs kEGP and feed-in tariffs kFIT. KPN corresponds to the criterion for grid relief. If the feed-in power PGrid is higher than the limitation PGrid, max, KPN rises
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as a linear function with the feed-in power. The third criterion KB considers battery aging effects. First the number of full cycles will be interpreted as costs. Second, the SOC dwell-time will also be associated with costs. Beginning at a SOC of 50 % with 0 € the costs rise linear to the SOC limits (SOCBatt, min and SOCBatt, max results 0.01 €/SOC-step). The objective function J has to be minimized over the time horizon T of the optimization. T
min J
¦ ij SOC,k
(3)
k 1
The constraints of the problem can be derived from the physical limitations of the lithium-ion battery. To ensure a safe battery operation the SOC and the power PBatt are limited as follows.
SOCBatt,min d SOCBatt d SOCBatt,max
(4)
PBatt, min d PBatt d PBatt, max
(5)
The formulated optimization problem is solved using dynamic programming. Referring to the principle of optimality proposed by Bellman in [16], the optimization problem was divided into sub-problems. Each sub-problem (find the lowest transition costs ij from SOCk to SOCk+1) was solved and then merged to formulate a total solution. Therefore, all possible charge trajectories from the initial SOC at the start of the day to the allowed lithium-ion battery states at the end of the day are evaluated. The SOC-trajectory with the smallest objective function value J presents the optimal battery charge strategy. This resulting strategy matches the optimum for the input data (PPV, pred, PLoad, pred) depending on the defined objectives, restrictions and discretization-steps. The quality of the optimization results generated with dynamic programming strongly depends on the prediction accuracy of the input data (PPV, PLoad). The correction of the optimization results due to bad predictions is the task of the reactive management module. The main idea is to accept power deviations PDev between the prediction values (PPV, pred, PLoad, pred) and the real values (PPV, PLoad) up to a certain limit.
PDev
PPV, pred PLoad, pred PPV PLoad
(6)
The integral of this power deviation PDev is approximately equivalent to a delta SOC. ǻSOCBatt
³ PDev dt
(7)
Based on the SOC-trajectory generated in the optimization module with the dynamic programming algorithm a SOC-bound r'SOC was build. Within the lower and upper bounds, the control of the lithium-ion battery follows the simple strategy that complies with the following two rules. If there is an energy surplus the lithium-ion battery will be charged. When energy is needed, the lithium-ion battery will be discharged. In this case the battery power PBatt is: PBatt
PPV PLoad
(8)
If the SOC reaches one of the bounds, the battery power PBatt is equal to ouput of the optimization module PBatt, The optimal range of the SOC-bounds will be analyzed in the following section. Fig. 3 illustrates a two day sample with a SOC-bound of 5 %. The graph on the top shows the power profile and the lower figure illustrates the SOC-bounds (grey) and the “actual” SOC (blue). pred.
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5000
PP V - PLoad
PGrid
PBatt
power in W
4000 3000 2000 1000 0
-1000 -2000
SOC in %
-3000 bounds
80 60 40 20
SOC
0
5
10
15
20
25 t in h
30
35
40
45
50
Fig. 3. Results of a two day sample with the SOC-bound method.
During night and morning hours the predicted SOC is similar following the simple rule-based strategy. About 9:00 am the sum of the difference between the prediction data and the real data is too high. Consequently the SOC reaches the upper bound. Now the SOC has to follow the upper SOC-bound to guarantee a time delayed charge of the lithium-ion battery. Despite of prediction errors the battery is fully charged before sunset without wasting energy through curtailment. During evening and night hours the lithium-ion battery supplies the electric energy demand. It’s conspicuous that the SOC tends within the SOC-bounds. In this example the optimization was carried at midnight (jump of the SOC-bounds due to new start-SOC of the optimization). The second day follows the same principle. 3.
Simulation results
The simulation input data for the PV and load profiles (four person household) are measured data from a reference object near Chemnitz. The dataset of the studied AC-coupled system introduced in section 2 is given in Tab. 1 including the physical limits and characteristic values which are necessary for dynamic programming. The adjustable parameters SOC-bound, optimization start-time and start-/end-SOC are determined in the respective subsection. Table 1. System parameters and assumptions. System specification
Simulation configuration
PV energy EPV
5000 kWh
Duration tSim
1 year
Electricity consumption ELoad
4000 kWh
Simulation time step tTimestep
1 min
Battery energy EBatt
5 kWh
Prediction horizon TPred
24 h
State of charge SOCBatt
0 % – 100 %
Optimization time step TOpt
15 min
Max. feed in power PGrid_max
2500 W
SOC discretization DSOC
0.005
Energy tariff KEGP
0.30 €/kWh
Feed in tariff KFIT
0.10 €/kWh
In order to evaluate the investigation results six performance criteria have been defined (14 – 19). Equations (9 – 13)
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introduce the basic energy-values PV energy EPV, electricity consumption ELoad, energy fed into the grid EGrid, f, energy consumed by the grid EGrid, c, and the curtailemnt losses ECurt. Table 2. Definition of Energy-values and performance criteria for PV battery system operation. Name
Equation
PV energy EPV
ܧ ൌ න ܲ ሺݐሻ݀ݐ
Electricity consumption ELoad
ܧௗ ൌ නȁܲௗ ȁ݀ݐ
(10)
Energy fed into the grid EGrid, f
ீܧௗǡ ൌ නȁ ሺܲீௗ ሺݐሻǡ Ͳሻȁ݀ݐ
(11)
Energy consumed from the grid EGrid, c
ீܧௗǡ ൌ නȁ ሺܲீௗ ሺݐሻǡ Ͳሻȁ݀ݐ
(12)
Curtailment losses ECurt
ܧ௨௧ ൌ නห ሺܲீௗ ሺݐሻ െ ܲீௗǡ ௫ ሺݐሻǡͲሻห݀ݐ
(13)
ܧௗ െ ீܧௗǡ ݇ௌௌ ൌ ܧௗ ܧ െ ܧ௨௧ െ ீܧௗǡ ݇ௌ ൌ ͳͲͲΨ ή ܧ ܧ௨௧ ݇ோ ൌ ͳͲͲΨ ή ܧ
(14)
Economic parameter kEc
݇ா ൌ ீܧௗǡ ή ܭாீ ீܧௗǡ ή ܭிூ்
(17)
Battery full cycles kBatt, fc
݇௧௧ǡ ൌ
Specific battery stress value kBatt, s
݇௧௧ǡ௦ ൌ ͳͲͲΨ ή නሺܱܵܥ௧௧ ͻͲΨሻ݀ݐ
Self-sufficiency kSS Self-consumption kSC Grid relief factor kR
(9)
(15) (16)
ȁܲ௧௧ ȁ݀ݐ ܧ௧௧
(18) (19)
Fig. 4 illustrates the results of the optimization start-time and start-/end-SOC sensitivity analysis related to the six performance criteria performed with the persistence-forecast. The start-/end-SOC varies between 0 % and 100 %. The start-time TStart of the optimization varies between 0 and 24 o’clock. The prediction horizon TPred was set to 24 h. The best value shows the green cross and the worst value shows the red cross. Self-sufficiency k SS
0
8 12
+ 30
20 28 0
(d)
20
40 60 SOCBatt in %
80
+
+
20
+
+
380
20 20
40 60 SOCBatt in %
80
100
time of day in h
8 12
0
20
40 60 SOCBatt in %
80
16
+
+
+
180
12 16
+ 0
20
40 60 SOCBatt in %
80
0
20
40 60 SOCBatt in %
80
100
(f) Specific battery stress value k Batt, s 0
4 8
24
8 12
24
100
Battery full cycles k Batt, fc
20
4
20
200
time of day in h
12
26
0
4
24 0
34
(e)
0
16
8
24
100
Economic parameter k Ec
32
Grid relief factor k R 0
30
4
16
(c)
time of day in h
16
time of day in h
time of day in h
+
4
24
Self-consumption k SC
(b)
0
time of day in h
(a)
100
4 8
+
12
+
16 20 24
0
20
40 60 SOCBatt in %
80
100
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Fig. 4. Results of the optimization start-time and start-/end-SOC sensitivity analysis. The green cross shows the best value and the red cross shows the worst value.
45
+
40 35 30 25
0
400
20 40 60 80 100 SOC-bound in % (d)
350 300
+
250 200 150
0
20 40 60 80 SOC-bound in %
100
65
(b)
60 55
+
50 45 40
0
300
20 40 60 80 100 SOC-bound in % (e)
260
+
220 180 140 100
0
20 40 60 80 100 SOC-bound in %
Grid relief factor k R in %
(a)
7.5
(c)
7.25 7 6.75 6.5 6.25
Spec. battery stress value k Batt, s
Self-consumption k SC in %
50
Battery full cycles k Batt, fc
Economic parameter k Ec in €
Self-sufficiency k SS in %
The highest self-sufficiency rate in Fig. 4(a) and the highest self-consumption rate in Fig 4(b) can be reached with an optimization start-time at 1:00 pm and a SOC of 80 % – 90 %. The best relief factor in Fig. 4(c) can also be found at a high SOC during midday. An unfavourable grid relief factor results starting the optimization at 4:00 pm with a SOC about 5 %. Looking at the electricity cost in Fig. 4(d) the best values can be found at 2:00 pm with a SOC of 90 %. Fig. 4(e) illustrates that the battery full cycles are nearly independent of the optimization start-time. The lowest number of battery cycles is reached for a SOC of 45 %. Fig. 4(f) shows the specific battery stress factor. Here, the best value can be obtained by starting the optimization at 3:00 pm with a SOC of 10 %. Noticeable is the steep rise of the values with a SOC of 80 %. Considering all six performance criteria it can be said that an optimization start-time in the evening at 5:00 pm with a start-SOC of 80 % produces the best results. The second investigation illustrates the results concerning the sensitivity analysis of the SOC-bounds (0 % – 100 %). A SOC-bound of 100 % corresponds to the rule-based strategy described in section 2. A SOC-bound of 0 % means that the SOC-trajectory generated by the dynamic programming algorithm must be maintained. An investigation of the prediction horizon has shown that the results of the six performance criteria rises with an increasing prediction horizon. Based on this investigation the prediction horizon TPred is set to 30 h and the daily optimization starts at 5:00 pm. Fig. 5 illustrates the simulation results for each performance criterion.
+ 0
25
20 40 60 80 100 SOC-bound in % (f)
20 15 10 5 0
+ 0
20 40 60 80 100 SOC-bound in %
Fig. 5. Results of the SOC-bound variation.
It's evident that a SOC-bound of 0 % isn't a good choice. The electricity costs are too high, self-consumption and self-sufficiency are not acceptable. The red point at a SOC-bound of 20 % leads to a compromise between the battery aging criteria (Fig. 5(e) and Fig. 5(f)) and the electricity cost Fig. 5(d). With this adjustment the battery full cycles are not higher than for the rule-based strategy. Furthermore, the electricity costs are about 50 € higher, but the battery aging will be slowed down by avoiding disadvantageous SOC's.
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4.
Conclusion
The paper has presented an optimizing model-based EM for a PV battery system consisting of a prediction module, an optimization module, and a reactive management module. Highlighted in this paper was the innovative reactive energy management. Simulation results show the sensitivity of the start/end-SOC and the optimization starttime towards the six defined performance criteria. Additionally, a sensitivity analysis of the SOC-bounds shows for a tolerance-band of 20 % good results related to electricity costs, battery lifetime, and curtailment losses. Currently, adaptive optimization techniques including further optimization criteria are investigated. In ongoing research projects the EM will be tested and benchmarked with other management strategies. Moreover, the EM will be integrated in the intelligent sizing algorithm employing particle-swarm-optimization [19, 20]. References [1] [2]
[3] [4] [5]
[6]
[7] [8]
[9] [10] [11] [12] [13]
[14] [15] [16]
[17]
[18] [19]
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