Optimized Operation of PV/T and MicroCHP Hybrid Power Systems
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Abstract
Specialists generally agree that Distributed Energy Resources (D E R s) will play a key role in the next generation power systems. Photovoltaic (PV) solar panels are very important energy conversion methods, yet they suffer from low energy conversion efficiency, availability issues and fluctuating output. Photovoltaic/Thermal (PV/T) has been introduced as a way to increase the efficiency of the system by utilizing the cogenerated heat. Combining PV/T with Combined Heat and Power (C H P) units is considered as a promising approach to encounter the intermittent and availability issues of solar energy. Smart grids, on the other hand, create opportunities for intelligent coordination between the different elements in the power grid. In this technologically focused paper we study the optimal operational strategies of coupled D E R s and storage within different scenarios. At the beginning we show the optimal sizes of different components, taking into consideration loads and investment costs. We introduce an approach to optimize the usage of the battery in which a controller tries to hold the battery near the optimal level and avoids unnecessary discharge operations. Furthermore, we explore the usage of feedforward artificial neural networks to estimate the demand. Starting with simple setups (i.e., only PV and Battery) and going then to more complex setups (i.e., with μ C H P), we have shown through comprehensive simulation studies that it is possible to enhance the profit when the optimized approach is applied.
Keywords
Distributed Energy Resources Photovoltaics μCHP Optimization Smart gridIntroduction
D E R s such as photovoltaic (P V) panels, micro turbines and windmills provide technologically feasible solutions to the current environmental challenges created by the current dominance of fossil fuelbased electrical power generation [29]. Nevertheless, these types of sources suffer from two main problems. Firstly they have usually low efficiency and secondly, most of them, especially PV and windmills, suffer from a high rate of uncertainty and therefore they are difficult to control. Additionally, some of them are not available all over the time, e.g., solar energy is not available in the night. To encounter the first problem, the concept of cogeneration of power is applied. Because μ C H P generates electricity and heat simultaneously, it is an efficient way to supply energy.
The P V/T concept provides an opportunity to increase overall efficiency of PV panels by making use of waste heat generated in the PV module. Because increasing the temperature will decrease the voltage, the efficiency of a PV solar cell decreases with the increase in the operating temperature and hence cooling is beneficial. PV cooling may be achieved by circulating a colder substance, water or air, at its rear or front surface or both surfaces. In P V/T systems, solar thermal collectors are combined with PV cells to form hybrid energygenerating units that simultaneously supply the two types of energy required by most consumers, heat and electricity. Combining controllable D E R s with renewable energy sources tackles the second problem such that it reduces the effect of fluctuation and availability issues. Furthermore, adding energy storage units will also reduce the effect of uncertainty of renewable energy sources and enhance their sustainability. The work in [29] showed that combining PV and μ C H P not only has the potential to radically reduce energy waste in the status of electrical and heating systems, but it also enables the share of PV to be expanded significantly.
According to the United States Federal Energy Regulatory Commission, demand response is a tariff or program established to motivate changes in electricity use by enduse customers in response to changes in the price of electricity over time, or to give incentive payments designed to induce lower electricity use at times of high market prices or when grid reliability is jeopardized [31]. Nevertheless, in the literature other definitions can be found. The focus of this paper is on pricebased demand response which can be employed to reduce power demand on high demand periods by introducing a variable price during the day [28]. The basic idea is to introduce a high price in the high residual demand periods and a lower price in the low residual demand periods. This approach encourages end users to shift some of the demand from high demand periods to low demand periods. Depending on internal and external conditions such as demand, weather, and price, they can decide to buy, store or sell electricity with various strategies in order to come close to selfsufficiency or in order to decrease costs or even achieve profit. The more households will be enabled with such possibilities, the more this will have an impact on the business model of utility companies. In order to investigate such effects, a combined simulation and optimization model of a network of such houses connected to a utility company is presented in this paper.
Because PV has a higher feedin tariff than μ C H P, a simple strategy for houses equipped with photovoltaics and μ C H P is to just feed all electricity into the grid which is generated by the solar modules, to use the electricity produced by μ C H P to cover local demand, and to buy needed electricity from the utility company which can’t be covered by μ C H P. This is an attractive option if the feedin tariff for the electricity produced by the PV is high and the price to buy electricity is low enough. However, feedintariffs get lower and electricity prices get higher. Prices for batteries are getting lower, and hence, using them eventually becomes an attractive option. Another simple operation strategy is to try to achieve selfsufficiency: the demand is first tried to be satisfied from the solar module and μ C H P, then by the battery, and at last option by the grid. Excess charges first the battery and if this is not possible is fed into the grid. A potential drawback of this selfsufficiency strategy is that it is probably not optimal, neither from the economical perspective of the single house, nor from the perspective of the national economics. Furthermore, the selfsufficiency strategy does not take the possibility of shifting loads into account.

We present an extended version of our previous work [4, 5, 6] that optimizes the profit from a hybrid energy system that has heat demand, P V/T, and μ C H P which were only partially investigated in our previous work.

We introduced a method to optimize the overall usage of the battery that takes into consideration not only the state of charge (SOC) but also the effect of charging/discharging cycles.

Taking electricity and heat demand and investment costs as inputs, we show the optimal size of each component.

In a comprehensive simulation study, we studied the savings when applying the optimized approach compared to a selfsufficiency based approach. We explored savings under different scenarios such as PV panel size, battery size, amount of elastic load and remuneration method.

We explored the effect of uncertainty in forecasted information and we provided a neural network base demand estimator.

We explored also the capability of the approach under system limitations such as battery size and elastic load requirements.
The rest of the paper is organized as follows. In Section Related Work we provide a summary about related works. In Section The Optimization Problem we present our approach and in Section Evaluation we evaluate the performance of the proposed scheme. Finally, Section Discussion and Conclusions concludes the paper.
Related Work
In [29] the author investigates the potential of deploying a distributed network of PV and CHP hybrid systems in order to increase the PV penetration level in the U.S. The temporal distribution of solar flux, electrical and heating requirements for representative U.S. single family residences were analyzed and the results show that hybridizing CHP with PV can enable additional PV deployment above what is possible with a conventional centralized electric generation system. The technical evolution of such PV+CHP hybrid systems was developed from the nearmarket technology through several generations, which enable high utilization rates of both PVgenerated electricity and CHPgenerated heat. The author derived a method to determine the maximum percent of PVgenerated electricity on the grid without energy storage. The results show that a PV+CHP hybrid system not only has the potential to radically reduce energy waste in the status quo electrical and heating systems, but it also enables the share of solar PV to be expanded significantly.
The authors in [26] use game theory to formulate an energy consumption scheduling game, where the players are the users and their strategies are the daily schedules of their household appliances and loads. They assumed that the utility company can adopt adequate pricing tariffs that differentiate the energy usage in time and level. They have shown, that for a common scenario, with a single utility company serving multiple customers, the global optimal performance in terms of minimizing the energy costs is achieved at the Nash equilibrium of the formulated energy consumption scheduling game. The study in [30] utilizes smart meter readings to implement smart control of μ C H P, storage, and demand response in microgrids. The work in [12] introduces an analysis framework and a relevant unified and synthetic MixedInteger Linear Programming optimization model suitable for evaluating the technoeconomic and environmental characteristics of different Distributed MultiGeneration (DMG) options. The authors in [20] proposed a strategy aimed at demand response for more intelligent control of μ C H P systems. This work is similar to our work in terms of using dayahead prices to optimize the operation of a house, nevertheless they focus on demand response with respect to heating systems, while our work takes into consideration hybrid systems with PV, μ C H P and power storage units. Additionally, our approach considers the costs of battery usage and explores the impact of uncertainty on the savings. The work in [13] presents PV selfconsumption as an approach for Active DemandSide Management for the residential sector. The authors then used neural networks to enhance the use of local generated power [22]. The authors in [14] formulated a linear optimization problem to identify the optimum daily operational strategy for the windhydro storage plants. Wind power was assumed as deterministic in [14], while in [27] forecasted wind power was represented as a stochastic variable.
In [19] a mixedinteger linear programming (MILP) model of the energy management structure is provided to investigate a collaborative evaluation of dynamicpricing and power limiting based demand response strategies. The author has considered Electric Vehicles (EVs) with bidirectional power flow capability and Energy Storage Systems (ESSs). [32] discusses the potential to increase PV selfconsumption through scheduling of household appliances in 200 Swedish singlefamily buildings. The authors in [15] used linear programming to efficiently compute a deterministic scheduling solution without considering uncertainties. To handle the uncertainties in household appliance operation time and energy consumption, a stochastic scheduling technique, which involves an energy consumption adaptation variable, is used to model the stochastic energy consumption patterns for various household appliances.
The impact of adding an electric storage system to a house equipped with a combination of renewable heat and electricity generation is investigated in [17]. For this purpose a linear mathematical program is given and solved by MATLAB for several periods of four days. The objective is to minimize the energy costs for consumed electricity and gas. As deterministic input for renewable energy conversion, energy demand, and wholesale spot prices, measured values are used together with demand profiles. The work in [11] addresses the problem of modelling the uncertainty of the input data, such as solar irradiation or temperature profiles. The linear program for households with PV and battery is solved for one year with the objective to reduce the energy costs. In contrast to our work, a flat electricity tariff is assumed.
To identify the optimum daily operational strategy to be followed by PV systems, a prediction of daily solar power generation is required. The values of insolation (solar irradiation) are the most important parameters for the solar energy applications. Some approaches to forecast solar power generation are focused on numerical weather prediction models [21]. Others are focused on predicting solar radiation from satellite images of cloud movements [25]. Several methods have been proposed to forecast power demand. The survey in [1] discusses some approaches such as multiple regression, exponential smoothing and iterative reweighted leastsquares which can be used to predict power demand. In [33] an ARMAX model for short term load forecasting and in [7] neural networks are used to estimate household electricity consumption.
The Optimization Problem
The household controller maximizes the corresponding revenue by using the battery (charging/discharging) or by exchanging power with the grid. Households exchange power with the main grid at market price. Additionally, the controller coordinates the work of the μ C H P such that it provides the maximum profit.
Summary of the model nomenclature
Component  Paramter  Summery  Unit 

η _{ c }  Battery charging efficiency    
η _{ d }  Battery discharging efficiency    
P _{ c }(t)  Power charged in the battery at time t  kW  
P _{ d }(t)  Power discharged from the battery at time t  kW  
\(P_{c}^{max}\)  Max charge power  kW  
\(P_{d}^{max}\)  Max discharge power  kW  
E(t)  Battery SOC  kWh  
Battery  E ^{ m a x }  Battery Capacity  kWh 
E ^{ m i n }  Min SOC  kWh  
E _{ o p t }  Optimal battery SOC recommended by the manufacturer  kWh  
ζ  Battery cost  €  
Γ  Battery lifespan  years  
ω  Battery cycles    
α _{ b }  Selfdischarge of the battery    
P _{ c h p }(t)  Power consumed by the CHP at time t  kW  
P _{ c h p−e l e }(t)  Electrical power generated by the μ C H P at time t  kW  
P _{ b o i l e r }(t)  Power consumed by the boiler at time t  kW  
P _{ s−c h p }(t)  Power exported to the grid from the μ C H P  kW  
C _{ f−c h p }  μ C H P electricity feedin tariff  €  
T _{ m i n }  Min temperature in the heat storage  Celsius  
T _{ m a x }  Max temperature in the heat storage  Celsius  
η _{ c−h e a t }  Heat storage charging efficiency    
μ CHP  η _{ d−h e a t }  Heat storage discharging efficiency   
η _{ p−h e a t }  Percentage of heat from the μ C H P    
C _{ h e a t }  cost of heat  €  
\(P_{chp}^{max}\)  Max power of the μ C H P  kW  
C _{ c h p }  μ C H P Power costs  €  
α _{ h }  Selfdischarge of the heat storage    
P _{ c h p−h e a t }(t)  Heat power generated by the μ C H P  kW  
P _{ c−h e a t }(t)  Heat power charged to the heat storage  kW  
P _{ d−h e a t }(t)  Heat power discharged from the heat storage  kW  
P _{ l−h e a t }(t)  Heat load at time t  kW  
H(t)  Heat energy storage level at time t  kWh  
H _{ m i n }  Min heat energy in the heat storage device  kWh  
H _{ m a x }  Max heat energy in the heat storage device  kWh  
C _{ h e a t }  cost to generate heat  €  
P _{ p v }(t)  Electrical power generated from the PV  kW  
PV/T  P V T _{ h e a t }(t)  Total solar heat generated by the PV/T  kW 
P V T _{ h e a t−u s e d }(t)  Used heat generated by the PV/T  kW  
P V T _{ h e a t−d i s c a r d }(t)  Discarded heat generated by the PV/T  kW  
P s−p v(t)  PV electricity soled to the grid at time t  kW  
C _{ f−p v }  PV electricity feedin tariff  €  
T  The optimization time horizon is (number of time steps)    
δ  Time step  hour  
C(t)  Electricity price at time t  €  
\(P_{e}^{max}\)  Max allowed elastic load  kW  
P _{ l }(t)  Load at time t  kW  
P _{ e }(t)  Elastic load allocated at time t  kW  
P _{ p h a s e s }(k)  Elastic load with k phases  kW  
P _{ b }(t)  Power bought from the grid at time t  kW  
β _{1}  Constant    
β _{2}  Constant    
P V T _{ c }  Cost of PV per time period  €/day  
B a t _{ c }  Cost of Battery per time period  €/day  
C H P _{ c }  Cost of CHP per time period  €/day  
P V T _{ o s }  The optimal size of the PVT  kWp  
B a t _{ o s }  The optimal size of Battery  kWh  
C H P _{ o s }  The optimal size of μ C H P  kW  
EL  Elastic Load  kWh  
[T _{1},T _{2}]  Elastic Load period  hours 
Two modes of operation are mainly responsible for reducing the lifespan of a battery; first keeping the battery at low SOC for long time and second the frequent charge and discharge. Therefore, the battery costs in Eq. 4 can be explained as follows. The first part represents the costs due to keeping the battery at low storage level. If the battery is kept at the lowest level for Γ hours, the battery will not be useable (the value of the battery will be 0 and the cost will be ζ). For example, for a 5 kWh battery (and optimal SOC is 5 kWh) with 3 years lifespan if the battery is hold at 0 kWh SOC, then after one hour at 0 kW SOC, the value of the battery will be reduced by \(\frac {1}{3*365*24}\). It is important to say, that holding the SOC of the battery at 1 kWh lower than the optimal SOC for 5 hours doesn’t have the same effect as holding the battery at 0 kWh SOC for 1 hour. Therefore β _{1} is usually less than one. The second part of Eq. 4 is for limiting the number of charging and discharging operations. A battery with ω cycles can be discharged from full to empty ω times. Therefore, the value of the battery will be 0 and hence the cost is ζ if the battery has been discharged ω×E ^{ m a x } k W h. For example, consider a 5 kWh battery with discharge capability of 1 kW and 1200 cycles, then after \(\frac {5}{1} \times 1200\) hours of discharging, the value of the battery will be 0. In other words, discharging the battery with 1 kW over one hour reduces the value of the battery by \(\frac {1}{5\times 1200}\). Of course, this is the worst case, i.e., continued discharging until the battery is empty. However, doing charging and discharging on high SOC levels will cause lower cost and hence β _{2} is usually less than one. We assume here that the optimal value of the state of charge is provided by the manufacturer and hence the optimization approach will try to keep the battery SOC near this value. In the simulation it is assumed 65 % (i.e. 3.25 kWh) is the optimal value of SOC of a 5 kWh battery.
The temperature inside the heat storage unit should stay between two temperatures T _{ m i n } and T _{ m a x } and hence the heat energy must stay between the two heat energy levels H _{ m i n } and H _{ m a x }.
The discrete value of x(t) can be 0 or 1. In each time slot, the battery is either in charge (0) or discharge (1) state.
Evaluation
Simulation Environment
We have used the simulation toolbox presented in [4, 5, 6, 8, 9] which is based on the AnyLogic [2] simulator. To build the simulation model of the electrical and heat components such as PV, μ C H P, and demand models as well as models for communication components, we have extended the components of the toolbox. Additionally, we relied on MATLAB [23] to solve the optimization problem. The data exchange between MATLAB and AnyLogic is done through a proxy. The simulation model defines first the topology of the smart grid which includes the power as well as the communication infrastructures. The main building blocks of these topologies are node modules (houses), which include models for electricity demand (e.g., refrigerator), supply (e.g., PV) as well as storage (e.g., battery).
For the electricity demand profiles, the mean energy consumption of households is used. Out of these profiles values are sampled and superimposed with stochastic functions to model the stochastic behavior of a single household [20]. For the solar model module, a solar insolation model is required. This model is implemented according to [24]. Weather profiles are used and superimposed with stochastic functions.
Parameters used in the simulation, default parameters are in parentheses
δ  (1 hour) & 15 min 
Efficiency charge/discharge of Battery  (77 %), 90 % 
\(P_{c}^{max},P_{d}^{max}\)  1 kW 
Max extra load \(P_{e}^{max}\)  1 kW 
Storage Capacity E ^{ m a x }  1, 2.5, (5), 10 kWh 
Network Size  20 
Area of Solar Module  10m ^{2}, (20m ^{2}), 40m ^{2} ,80m ^{2} 
Efficiency of Solar Module (Electricity)  0.1 
Efficiency of Solar Module (Heat)  0.7 
Elasticity  (0 %), 5 %, 10 %, 20 % , 2kWh 
Battery Cost  (0), 100 €/kWh, 140 €/kWh 
(T _{ m i n },T _{ m a x })  55 , 85 C 
η _{ d−h e a t },η _{ c−h e a t }  100 % 
η _{ p−h e a t }  70 % 
\(P_{chp}^{max}\)  4 kW 
α _{ h }  2 % 
α _{ b }  0 % 
C _{ f−p v }  (0.18) & 0.1 € 
C _{ f−c h p }(t)  0.09 € 
C _{ c h p }  0.07 € 
Electricity Market  (Simple Market), EEXMarket 
Dayahead Price
To simulate the dynamic nature of the dayahead electricity prices, we relied on real historical data from the European Energy Exchange in Leipzig as in [4, 5, 6]. We developed two types of markets to show a variable enduser electricity price. The main goal of these markets is to try to answer the following question: If there were dayahead prices available for endusers, how would they look like? The first market tries to reflect demand/supply on the price while the other market tries to use real data to figure out the dayahead price.
Simple Market
In the first electricity market we used the difference between demand and supply in the network to figure out the dayahead price, i.e., high demand leads to high price and low demand leads to low price. In this simple electricity market, every controller sends hourly its forecasted amount of energy demand and supply for the rest of the day to the server. With the received data and electricity price limits as in [4, 5], the server calculates the day ahead price and sends it to the consumers. To simulate variable electricity prices, a simplified representation of the electricity market is used in the model. The server uses the history of the difference between residual demand and supply (D e m a n d−S u p p l y) to determine the price such that the maximum difference corresponds to the maximum price and the minimum corresponds to the minimum price. The electricity price changes during the day depending on the actual demand and supply, therefore the server sends dayahead electricity prices to the consumers every 24 hours.
EEXbased Market
We performed four sets of experiments to explore the effect of different parameters on the savings. We started with a simple setup where we considered only a system with PV and Battery. Then we explored the effect of battery costs and optimal usage of the battery. After that we investigated a more complex system where we included PV/T and μ C H P. Final we explored the effect of uncertainty of the demand forecast.
Optimal System Setup
Summary of the different unit costs
Component  Cost  Typical Size  Life Span 

PV/T  3000 €/kWp  130 kW  20 years 
Battery  140 €/kWh  120 kWh  4 years 
μ C H P  4000 €/kW  120 kW  18 years 
The Optimal Size of the Different Components
Setup  Component  Size  Notes 

PV/T  9.8 kWp  
Stand Alone  Battery  10.2 kWh  
μ C H P  4.1 kW  
PV/T  10.3 kWp  PV feedin tariff  
Grid Connected  Battery  3.9 kWh  0.1 €/kWh 
μ C H P  4.0 kW  
PV/T  30 kWp  PV feedin tariff  
Battery  1.8 kWh  0.18 €/kWh  
μ C H P  4.0 kW  
PV/T  10.5 kWp  PV feedin tariff  
Battery  4.6 kWh  0.1 €/kWh  
μ C H P  4.0 kW  flatrate electricity price 0.29 €/kWh  
PV/T  3.7 kWp  PV feedin tariff  
Battery  2.3 kWh  0.1 €/kWh  
μ C H P  4.9 kW  Winter  
PV/T  30 kWp  PV feedin tariff  
Battery  2.4 kWh  0.1 €/kWh  
μ C H P  0.23kW  Summer 
Savings Due to Electricity Management Excluding Battery Costs
At the beginning we start by considering only the electricity and excluding the heat energy. Additionally, we used the load models as described in [4, 5, 8]. The feedin tariff for PV electricity is 0.18 €/kWh.
Figure 4b shows the savings due to shifting loads partially. As it can be seen, the savings increase as we increase the elastic load. The controller uses the dayahead price, supply forecast and load forecast to find the appropriate time slot to allocate the elastic load.
Savings Due to Electricity Management Including Battery Costs
Savings Due to Electricity and Heat Management
Figure 6b shows the amount of electricity that has been produced by the μ C H P and exported to the power grid. The compensation for electricity produced by the μ C H P and fed to the grid is lower than the feedin tariff for PV and the price of electricity bought from the power grid. Therefore, the only situation where the electricity produced by the μ C H P will be exported to the network is when the local electricity demand is already covered and the battery is full. This situation can occur in winter, when the μ C H P is used heavily to cover the heat demand.
Electricity Demand Estimation
Limitations
The main limitation of the model is simplification of some components. For instance, all models are linear; e.g., the investment costs are considered as linear. The simulation model of the battery is very simple and it does not take into consideration parameters such as temperature and the effect of the SOC on the charging and discharging power. Another simplification is the electricity market. In our approach, neither the time value of money nor the correlations between weather, PV generation, and demand have been considered. Moreover, the electricity market modeling approach is strongly simplified. Additionally, the simulation model of the μ C H P is also simple and therefore it does not include issues such as power ramps. The PV model does not consider the outside temperature. Furthermore, the neural network was trained offline only. The main reason behind these simplification is to keep the system linear and hence easy to be implemented inside an embedded microcontroller (i.e., inside the smart meter). In fact, a dynamic (nonlinear) model for a battery would be necessary if network dynamics are going to be studied. If energy providers want to use a pricebased DR program and motivate the people to shift their demand from high demand period to low demand periods, they should provide a variation in the price that makes the load reallocation profitable. Therefore, we employed a method that makes the household electricity price signal to have a similar shape as at the EEX market.
Discussion and Conclusions
We presented a technologically concentrated approach to maximize the profit of privately owned PV/T and μ C H P hybrid power systems. The optimization problem is formulated as linear programming which makes it easy to be implemented inside a smart meter or in an energy management controller. The approach requires forecasts for demand and supply. At the beginning we assumed that these forecasts are available through services from an external system. In an extensive simulationbased performance evaluation, we assessed the impact of battery size, the panel size, and demand elasticity on the profit maximization. We compared the savings of the proposed optimization approach with a selfsufficiency approach. The results clearly demonstrate the possibility to enhance the profit when applying the optimized approach. The results show also that a larger battery does not necessarily yield more savings. This is due to the fact that it is not allowed to resell the energy bought from the grid. We then included the cost of the battery such that the battery SOC remains near the optimal SOC recommended by the manufacturer. Additionally, the battery cost term prevents unnecessary charge and discharge operation. Furthermore, we introduced an artificial neural network as a candidate for demand estimation and the results show that the estimation error has no significant impact on the savings. The reason behind that is mainly because the approach depends heavily on the dayahead price, which has no error. Additionally, it is sufficient to know the trend of the demand, i.e. low demand in the midday and high demand in the early evening.
Notes
Acknowledgments
Peter Bazan is also a member of “Energie Campus Nürnberg”, Fürther Str. 250, 90429 Nürnberg. His research was performed as part of the “Energie Campus Nürnberg” and supported by funding through the “Aufbruch Bayern (Bavaria on the move)” initiative of the state of Bavaria.
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