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Impacts of electricity grid tariffs on flexible use of electricity to heat generation
Energy xxx (2016) 1e9
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Impacts of electricity grid tariffs on flexible use of electricity to heat generation Jon Gustav Kirkerud*, Erik Trømborg, Torjus Folsland Bolkesjø Norwegian University of Life Sciences, Department of Ecology and Natural Resource Management, Norway
a r t i c l e i n f o
a b s t r a c t
Article history: Received 1 December 2015 Received in revised form 13 June 2016 Accepted 18 June 2016 Available online xxx
District heating plants having both electric boilers and alternative fuel options could hold a key in providing flexibility needed for cost efficient integration of variable renewable power. The electricity grid tariff is an important component of the electricity costs of electric boilers, and these tariffs may promote or hamper flexible use of power-to-heat. In this paper, a mixed integer cost minimization model that schedules the operation of different boilers in a district heating plant is developed and applied to analyze the impact of different tariff structures on flexibility provided by electric boilers. The results confirm that the structure of electric grid tariffs significantly influences the flexibility provided and the annual shares of electric boiler use, caused by differences in grid tariff structures, vary from 2% to 17%. Novel tariff structures with time-varying elements increase utilization electricity in low price periods and improve the profitability of power-to-heat as a flexibility solution. The study clearly demonstrates that system effects should be considered when grid tariffs for flexible electric boilers are designed and that novel tariff designs should be more widely adapted. © 2016 Elsevier Ltd. All rights reserved.
Keywords: District heating Power-to-heat Variable renewable energy integration Mixed integer model Grid rent
1. Introduction New variable renewable energy (VRE) sources are increasing their share in worldwide electricity generation as a result of a need to decrease fossil-based power generation, while maintaining energy security. It is well known that high VRE shares cause challenges in load regulation, since the VRE supply cannot be regulated and storage of electricity has high costs. A recent review study [1] concludes that increased integration of thermal and electric systems (P2H) is promising for provision of flexibility needed for renewable power integration. District heating plants (DHP) with several fuel options can provide such flexibility if electricity is used for heating in periods with high power supply and low demand and other sources such as biomass is used when demand is high relative to supply. P2H in DHP has a large potential; for example in the Nordic region the DH generation is around 130 TWh, which correspond to about 30% of the size of the Nordic electricity market [2]. Electric boilers (EB) and heat pumps (HP) are mature P2H technologies available in the market. EB is in general more suited for flexibility purposes than HPs since the HPs have the economic
* Corresponding author. P.O. Box 5003, NO-1432 Ås, Norway. E-mail address: [email protected] (J.G. Kirkerud).
characteristics of a base load technology e high investment costs and low operational costs [3]. The benefits of using EB in DHP for VRE integration has been addressed in several previous studies [4] strongly recommends using electricity and heat market interaction for increased energy system flexibility [5] studies the consequences of introducing these technologies into central cities in the Nordic energy market and concludes that it benefits the integration of wind power and saves fuel costs for heat producers. Also, [6], concludes that electric boilers provide substantial flexibility, especially for VRE, and that HPs combined with heat storage is a good solution to integrate baseload. Cities or municipalities can use P2H strategies to increase their share of renewable energy, according to [7]. To fully exploit the flexibility potential from P2H, prices must be efficient and time varying [8]. The retail price of electricity relative to other fuels determine when and how the electric boiler is used in a DHP. This cost consists of three components: wholesale electricity price, transmission costs (grid rent) and taxes. Taxes are usually low for industrial customers [9]. Wholesale electricity costs is usually the largest part and is normally charged based on the hourly wholesale price of electricity. In competitive markets, the hourly wholesale price provides efficient price signals conveying the short-term marginal cost of electricity generation. Transmission cost is the second largest cost component of an EB and comprises
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according to [9] 20e50% of total electricity costs in European countries. An increase in VRE deployment can cause this cost to further increase as these sources are often located far from load centers [10]. District system operators (DSOs) cover allowed costs, determined by electricity market regulators, through grid tariffs. However, time variation of tariffs are often neglected, as tariffs must be carefully designed and consider the interest of the DSO, the consumers and economic efficiency. This conflict of interest partly cause substantial variations in the actual tariff structure between countries and between DSOs. Consequently, conditions for flexible use of P2H vary widely and is seldom optimal. The introduction of smart meters with real-time measurements, combined with the recent increase in deployment of variable renewables has actualized grid tariff designs that increase demandside flexibility. Real-time measurements allow for tariffs designs that are more sophisticated. High VRE shares cause high short-run volatility of electricity prices and distributed VRE reduce utilization of the grid for some customers [11]. Different options and suggestions for changes in tariff design, from different viewpoints, have been discussed in the literature. Arguing from a DSO perspective [12], promotes an arrangement where customers pay for a subscription to a certain amount of power. Such tariffs secure a predictable income for DSOs [13]. discuss and simulate the effects of tariff structures on end-customer benefits and find that time varying pricing will be most beneficial [14] analyzed empirical data of hourly-metered consumption by residential customers in Sweden on tariffs and found that better tariff design could shift consumption from high demand hours to low demand hours. Finally [15], studies tariffs through simulations of flexible households and argues for flexible tariffs that increase with the hourly withdrawal of power from the grid. This reduces simultaneous peaks in demand caused by low price hours. Several studies focus on tariff designs to reduce the individual consumer's maximum consumption rather than the network's maximum consumption. In this study it is assumed that the latter is a more important driver of network costs for large scale consumers such as district heating plants. Also, many previous studies analyze the response to tariffs by consumers with a low degree of flexibility such as residential and services sector, whereas this study analyze large and very flexible consumers such as DHPs that can fully replace electricity consumption on short notice at a low cost. This type of consumers could hold a key in handling variable supply from VRE. The objective of this study is to analyze how electricity grid tariff structures affect the use of electricity and hence the role of the heating sector as a flexibility provider. The study compare and evaluate alternative structures, representing a range of possible options, based on typical tariff design principles as well as the ability to enable flexible response of P2H to electricity prices. For this purpose, a new DHP mixed integer optimization model is developed. The model minimizes the operational costs and capture variations in electricity prices, start-up costs of different boilers in a heat only plant, as well as the characteristics of different grid tariffs.
Economic efficiency principles state that tariffs should give the right price signals for both consumers and DSOs so that the socio-economic surplus is maximized both in the short and long term. Tariffs should reflect each network user's contribution to network costs to achieve cost-causality. The equity principle means charging “each consumer the same amount for using the same good or service, independently of the electricity's use and of the customer's characteristics.” Consumer protection principles emphasize the need for transparency and stability in the tariff design method, and a simple and understandable tariff structure. These principles contravene each other and a reasonable compromise must hence be found. Typically, consumer protection principles has been used as an argument against more economic efficient tariffs [18]. A design with high degree of time-varying pricing, to satisfy economic efficiency principles, can be difficult to communicate and understand meaning that the consumer protection principles is challenged. One possible approach, presented in [18], is to have both a default tariff structure that favors consumer protection principles and an optional tariff structure that pursue economic efficiency principles. Flexible consumers or consumers with load patterns that avoid peak hours will benefit from the optional tariff, while other consumers benefit from the default. This study asserts the need to find tariff schemes that sustain good tariff principles while still allowing for flexible use of P2H, thus a tariff with high degree of efficiency is desirable. 2.2. Time varying tariffs The economics of tariff design is much discussed in the literature (e.g. Refs. [11,19,20]) The electrical transmission grid is a natural monopoly, as the capital costs (fixed costs) are high compared to the short-run marginal costs (SRMC) (variable costs), which are primarily costs to cover grid losses. Variable user charges should therefore be set low to ensure high grid utilization in hours where grid capacity is sufficient. However, the demand for transmission vary greatly over the course of a day and a year, and the grid must be dimensioned to meet expected peak demand. The long-run marginal costs (LRMC) of increasing transmission during peak situations include additional capital and operational costs of incremental capacity. The LRMC of increasing demand in off-peak situations is low in comparison as only SRMC of existing capacity id included. This gives a rationale for peak pricing which discriminate between consumption in off-peak and peak hours. In such a system, a low tariff - reflecting SRMC only e is given to consumers during off-peak hours, and a high price reflecting LRMC is given in peak hours. The design of the grid tariff is usually structured into three main components: Fixed access charge (V/period) Energy charge (V/kWh/period) Demand or capacity charge (V/kWpeak/period)
2. Grid tariff design 2.1. Principles for tariff design Picciariello [16] and Rodríguez Ortega [17] identify principles for tariff design, here summarized into three main groups: System sustainability principles state that tariffs should recover the allowed costs for the DSO. A tariff structure that secures a stable yearly income is usually preferred over one that vary greatly from year to year.
The fixed charge is the cost of access to the grid regardless of the consumption and covers the residual costs. The energy charge is a cost per kWh electricity consumed. At minimum, the energy charge should reflect the short-run marginal cost of transmission, i.e. the marginal cost of covering grid losses. To reflect time variation in loss factors and electricity prices, the charge may differentiate between seasons and peak/off-peak hours or be settled dynamically based on the electricity price. It can also be used to signal long term marginal costs through time-of-use or critical peak pricing structures [21].
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In the demand charge, also referred to as capacity charge, the cost per kW are calculated based on the maximum load level(s) during the billing period. They describe costs for grid well as these are to a high degree capacity related. Demand charges requires more advanced metering equipment and is therefore most common for larger customers. Some versions of this charge are based on a subscribed level decided by the customer [22] or even the fuse size. 2.3. Effects of different tariff designs A common tariff design for small consumers have typically consisted of an access charge and an energy charge, because advanced metering is required for demand charges. Known as flat rate tariffs, these designs have the advantage of simplicity, but lack peak pricing. Compared to peak pricing, a high flat rate tariff will disincentivize EB generation in off-peak hours and incentivize in high peak hours. Time-of-use differentiation or critical peak pricing (CPP) can add temporal granularity to the energy charge. In time-of-use tariffs, selected hours (e.g. 7am to 7pm on weekdays) have a higher tariff. CPP often builds on top of a time-of-use structure, but have an extra charge in a few critical peak hours per year (50e100) declared in advance by the DSO. Results from a CPP program that have been tested in California can be found in Refs. [23] and [24]. A real-time pricing (RTP) structure, where the energy charge is a function of the electricity price, has potential benefits. Electricity prices are most often high when the load level in the grid is high and thus reflect grid costs in a limited extent. Time-varying energy charges gives a predictable cost for DHP operators and it is easy to determine dynamic elements such as CPP or a link to power prices. One disadvantage is that grid costs translates better to capacity (kW) than energy (kWh) and hence demand charges might be better suited. A standard form of the demand charge, as used in [25], charges a fee on the highest measured demand level within a month combined with a fixed charge and an energy charge. This design is well suited when the consumer's individual peak correlates with the network peak. However, a DHP with different fuel options will try to avoid electricity use in the network peak because power prices tend to be high in high demand periods. Instead, a DHP should have highest electricity consumption in hours with low power prices and hence relatively low electricity demand. Under demand charges, the marginal cost of using electricity depends on the number of hours electricity use is profitable, leading to uncertainty and suboptimal use of EBs: A billing period with few off-peak hours with low prices leads to less EB use and therefore a high demand charge per energy unit. Inversely, in a billing period with many off-peak hours with low prices (e.g. caused by VRE), the demand charge will be allocated on many hours. In the high load hours in that billing period, the marginal demand charge in peak hours is zero and there is no economic incentive to reduce peak load. In this regard, the standard demand charge cannot be classified as economically efficient in a power system perspective. According to [26], designs similar to the described demand charge exhibit poor cost reflectiveness, but an improvement is to charge on the measured peak load within typical peak hours (such as in Ref. [14]). An even better alternative would be to charge only on the measured peak load within critical peak hours. A demand charge based CPP design is likely to give a more stable cost recovery for the DSO compared to CPP based on energy charges. In addition, the DSO can be allowed to declare critical peaks in more hours of the year as this will not likely increase costs for consumers.
3
3. Methods 3.1. Model description A mixed integer cost minimization model that schedules the operation of different boilers in a district heating plant for a full year is developed and applied, and the effects of different grid tariff on the use of an EB in a DHP are analyzed under different power price scenarios. Mixed integer linear programs are commonly used for unit commitment and scheduling problems in electricity system modeling, but e as shown in this study e they can also explain the DHP planning challenges. The model developed in this study minimizes one year of operational costs for a DHP plant considering fuel costs, start-up costs, electricity prices and grid tariffs. The optimization horizon is one year divided into 12 months, each with 728 h, which gives 8736 h for a full year. Perfect foresight is assumed within the optimization period. The typical unit commitment elements (Equations (1)e(8)) of the model are based on Sumbera [27]. Equations (9)e(11) are new in this study and treat the grid tariffs. In the following description the indices for month are excluded for readability. A simplistic flow chart of the model is shown in Fig. 1. The objective function (1) minimizes costs for fuel cft start-up cst and electricity cet
MIN
XT t¼1
f
ct þ cst þ cet
(1)
Heat generation pit from each boiler i and hour t is constrained by maximum boiler capacity (2) and heat load Lt must be met at all times by the generation from the boilers (3):
pit P max ; Lt
ci; ct
XI
p ; i¼1 it
(2)
ci; ct
(3)
Fuel costs are a function of the fuel price FPi heat generation and the boiler efficiency hi (4):
cft ¼
XI
FP i¼1 i
pit
hi
;
ci; ct
(4)
For the calculation of start-up costs, a binary on/off variable xit or each unit is defined in (5) and (6) together with feasible area of operation:
xit P min pit ;
ci; ct
(5)
pit xt P max ;
ci; ct
(6)
The value for the binary start-up variable yit given in (7) and is associated with start-up costs Cis . (8). For t ¼ 1 in (7) xit1 is replaced by the x value for the last hour xiT from last month.
xit xit1 yit ; cst ¼
XI
Csy ; i¼1 i it
ci; t > 1
(7)
ci; ct
(8)
The cost of electricity consists of four components (9). The cost of electricity bought on the spot market at market price EPmt electricity tax ETm, and the energy charge of the grid tariff are all given on a per MWh basis. The demand charge DC is calculated based on the highest hourly load during the optimization period pmax , which is an endogenous variable, defined in (10). In one tariff structure studied (CPP, explained below), t in Equation (10) is exchanged with a subset of t which only includes hours of network peak load.
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Fig. 1. Simplistic flow chart of the model.
cet ¼
pit
hi
ðEPt þ EC þ ETÞ þ
pmax
hi
3.3. Electricity price and grid tariff data
DC;
ct;
i ¼ electric boilers (9)
XI
p i¼1 it
pmax ;
ct; i ¼ electric boilers
(10)
In the dynamic energy component option (11) replaces (9). In (11) the energy component is a function of the electricity price and a tariff factor TF.
cet ¼
pit
hi
ðEPt ð1 þ TFÞ þ ETÞ þ
pmax
hi
DC;
ct;
i ¼ electric boilers (11)
3.2. Data and assumptions The modelled plant, with techno-economic data as described in Table 1, represents a typical small-scale DHP in Norway, having three boilers: a biomass baseload boiler burning woodchips, a peak load boiler burning LPG (liquid petrol gas), and an electric boiler. The assumed conversion efficiencies are the lower heating values for various fuels. Fuel prices include emission taxes. Minimum loading conditions is considered only for the wood chip boiler. The assumed annual heat consumption including distribution losses is 80 GWh and maximum load is 30 MW. The distribution of heat demand per hour originates from actual heat load data from 2012 collected from Hafslund Varme's grid in Oslo. These data incorporates heat demand primarily from households and services sector buildings.
The retail price of electricity consists of three components: wholesale electricity price, grid tariffs and electricity tax. The electricity tax is the smallest component amounting to 0.6 V/MWh (4.5 NOK/MWh) in the case study. The modelled DHP is assumed to respond to the hourly price variations of the day ahead wholesale market. Two different power price series are analyzed (Figs. 2 and 3), reflecting the observed prices in 2012 for the Oslo spot price region in Norway (NO1) as well as the Western Denmark price region (DK1) [28]. The power price in Oslo represents a typical price structure of a hydropower region while West Denmark represents one of a thermal power dominated region with substantial wind power as well. As expected, the Danish price exhibits more short term price variations, with relatively high peak prices during the mid-day (Fig. 3). Moreover, high wind power penetration causes additional price variability and sometimes also negative prices. The Oslo region has lower short-term power price volatility, but usually larger variations over seasons and years. As shown in Fig. 3, the electricity market spot price (excluding grid rent and taxes) exceeds for most hours the assumed SMRC (short-run marginal cost) of the biomass boiler, but it is lower than the SRMC of the LPG boiler. In Oslo during summer, the spot prices are lower than SRMC for the biomass boiler for much of the time e due to high run-of-river generation. In the following, the two price series is referred to as the HRP (hydro region price) and the TRP (Thermal region price). 3.4. Grid tariff structures analyzed This study considers two elements of the grid tariff: energy charges and demand charges. The access charge is disregarded, since it does not influence operation of the electric boiler. The
Table 1 Technical and economic assumptions for the modelled plant.a
Wood chip boiler LPG boiler Electric boiler a
Capacity PMax [MW]
Efficiency h
Fuel price FP [V/MWh]
Minimum load Pmin [MW]
Start-up cost Cs [kV]
15 15 15
85% 92% 98%
25 55 variable
3 0 0
375 0 0
The exchange rate used for converting from NOK (Norwegian Krone) to Euro is 7.48, the time weighted average exchange rate in 2012.
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Fig. 2. Assumed weekly average electricity spot prices and grid tariff rates. Grid tariff levels are collected from Hafslund nett [29](Oslo DSO). The demand charge is 14.7 V/MW in January, February and December, 6.3 V/MW in March and November, and 1.1 V/MW in summer months. The energy charge is 3.3 V/MWh from November through March and 2.0 V/ MWh in summer months.
Fig. 3. Average wholesale electricity prices compared to SRMC of fuel based boilers shown with hourly resolution over the week (V/MWh).
baseline energy and demand charge components of the grid tariff are shown in Fig. 2. These are charges used by the DSO in Oslo for high voltage commercial customers [29] (exchange rate: 1 V is 7.48 NOK). The charges are highest during the winter because high demand for electric heating in Norway cause system demand peaks and high marginal grid losses. Four different tariff structures are analyzed: i) A standard flat rate structure (FT), ii) a standard demand charge based structure (DC), iii) a demand charge based critical peak pricing structure (CPP), and iv) a dynamic energy charge structure related to the electricity price (RTP). Table 2 summarize the details of the analyzed grid tariff structures. This study emphasizes the effects of tariff structure changes, not changes in the overall grid tariff level. In the model simulations, the tariff structures are leveled to generate the same level of tariff income to the DSO for a customer with a load pattern similar to system load. The country consumption profiles for Norway and Denmark 2012 [28] are used for this purpose. It is assumed that the sum of individual peak loads is 25% higher than the system peak load to account for imperfect
correlation in peak demands. The flat rate tariff structure (FT) consists of the baseline energy charge (Fig. 2) plus 13.7 V/MWh in all hours to compensate for not having a demand charge. FT represent typical tariff structures for smaller consumers without hourly metering and serves as a baseline in this case study. The demand charge tariff structure (DC) consists of the baseline energy charge and the baseline demand charge. A fee is charged on the consumer's maximum load within the monthly billing period. Time of use within the month is insignificant and every hour can act as a calculation hour. Contrary, in the critical peak pricing tariff structure (CPP), only hours where the electricity system load is particularly high can act as a calculation hour. High system load is defined here as the 5% hours of the year with highest system electricity demand. Electricity consumption during other hours will not trigger the demand charge in this tariff structure. CPP has a yearly billing period for the demand charge with an associated higher charge, and also contains the baseline energy charge. The real-time pricing tariff structure (RTP) consists of an energy charge only, calculated as the function of a
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Table 2 Summary of the grid tariff structures analyzed. Tariff structure
Description
Energy charge
Demand charge
Demand charge calculation
FT
Flat rate tariff
None
None
DC
Baseline
Peak demand/utilized capacity per month
CPP
Standard demand charge Critical peak pricing
Baseline þ 13.7 V/ MWh Baseline Baseline
RTP
Real time pricing
Spot-price 46.4%
59.6 V/kW/ year None
Peak demand/utilized capacity per year in system peak hours (5% hours with highest load in 2012) None
tariff factor and the wholesale electricity price. The tariff factor is set to 46.4% to ensure level tariff structures. 4. Results 4.1. Annual heat generation in biomass, LPG and electric boiler for different tariff structures Fig. 4 shows annual heat generation share from each boiler and for each electricity price scenario and grid tariff structure. In all scenarios, the biomass boiler supplies at least 78% of total generation. The minimum load requirement for the biomass boiler imply that some energy (0%e1.6% of total yearly heat generation) is cooled off, i.e. wasted, in the summer when heat consumption is low. As expected, scenarios with high biomass generation have more heat cooled off. When the electric boiler generation increases, it replaces both biomass and LPG boiler generation. In both price scenarios, CPP cause the lowest share of biomass and LPG generation. The highest share of LPG generation occurs under the DC tariff structure and the highest share of biomass generation occurs under FT for hydro region and DC for thermal region. 4.2. Electric boiler generation pattern under different tariff structures Fig. 5aed displays the generation patterns of the EB under different tariff structures. The characteristics of the price profiles discussed in chapter 3.2 cause corresponding variations in EB generation patterns in the two price scenarios. In the HRP scenario, the EB generates most during summer months due to low
electricity prices in the summer. In the TRP scenario, more low price hours occurs during winter causing more EB generation in those periods. There is also a clear difference in the hourly pattern (Fig. 5c and d), with most EB use during daytime in the HRP scenario oppositely to the TRP scenario where most EB use occurs during nighttime. Different tariff structures cause significant differences to the generation patterns. Firstly, the demand charge tariff structure (DC) eliminate all electricity use during winter weeks for two reasons: the demand charge is high during winter (Fig. 2) and off-peak hours are not exempt of the demand charge. Even with negative prices during some winter weeks in the TRP scenario, the demand charge efficiently block EB use. All other tariff structures allows some winter EB generation with the CPP allowing most. A second observation is that energy charge based structures, FT in particular and to some extent RTP, cause low summer generation. For FT, this is a direct result of the imperfections of flat rate tariffs, which overprice consumption in low demand periods. The EB generation pattern variations over the hours of the day also display relevant features of the tariff structures. The DC and FT tariff structure greatly reduce nighttime generation in the TRP scenario due to their flat tariff structure. With the DC tariff structure, the ability for the EB to react to hourly power price variations is particularly high. A standard demand charge indifferent of the hour of consumption can be satisfactory when electricity prices have a clear seasonal variation, but little intra-day variations. However, with more wind power having high generation in some winter weeks, the inability of this charge to encourage flexible P2H becomes prominent. A standard energy charge structure also comes up short, as EB generation in off-peak hours are as expensive as in peak hours.
Fig. 4. Share of heat generation covered by each boiler in the hydro region price (HRP) and thermal region price (TRP) scenario. Grid tariff structures are defined in Table 2.
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Fig. 5. aed: Generation patterns of electric boilers over weeks (a and b) and over hours of day (c and d) for HRP scenario (a and c) and TRP scenario (b and d).
FT stimulates to relatively low use of EB in both electricity price scenarios with correspondingly low use in hours when the electricity price is low. As there is no charge on peak load consumption, some use occurs in hours with high system load. The tariff structure generates high income for the DSO, but moderate cost savings for the DHP. DC has a very different impact on EB use in the HRP and TRP scenario. DC cause high EB use in HRP scenario due to low cost in summer months with accordingly low income for the DSO. The price structure of the TRP scenario combined with the DC tariff structure cause the lowest EB of all scenarios and accordingly low DSO income. The income to the DSO is moderate in the HRP scenario as demand charges are kept to a minimum. The costs reductions for the DHP are high in the HRP scenario, but very low in the TRP scenario. CPP cause the highest EB use of all tariffs because demand charge is calculated from only 5% of hours and electricity is hence cheap in many hours. It is efficient in reducing generation
4.3. Impact of grid tariff structures on electric boiler use and operational costs Table 3 displays important output parameters when assessing the impact of tariff structure on EB use in a flexibility perspective. In a security of supply perspective, it is desirable to use less electricity in network peaks, defined in this study as the 5% hours of the year with highest load. If EB use causes more electricity generation by fossil power plants, it results in increased emissions. For flexibility purposes, it is advantageous with electricity use in low load hours, defined here as hours with spot prices below 20 V/MWh. The tariff structures are in addition evaluated on the revenues for the DSO and the economic benefit for the DHP [30]. DHP benefits are calculated as the difference in variable operating costs with or without the electric boiler installed. The average cost of electricity per unit allocated to the different cost components are shown in Fig. 6. The observations displays major differences in the EB use characteristics and economics:
Table 3 Result summary of the impact of the grid tariff strictures defined in Table 2.
Hydro region price scenario Total EB generation (MWh) - EB generation in network peaks (5% hours with highest load) - EB generation in low price hours (spot price < 20 V/MWh) DSO income (kV) Reduced DHP variable operating cost (kV) Thermal region price scenario Total EB generation (MWh) - EB generation in network peaks (5% hours with highest load) - EB generation in low price hours (spot price < 20 V/MWh) DSO income (kV) Reduced DHP variable operating cost (kV)
FT
DC
CPP
RTP
5539 373 2221 92.3 41.5
8363 e 3975 39.0 90.6
13,812 e 4201 33.7 176.5
8466 208 4061 90.1 78.6
4172 158 1837 70.9 55.1
1621 e 912 9.2 19.7
10,282 e 3459 30.5 151.2
5355 111 3204 38.1 100.9
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Fig. 6. Average annual electricity costs per MWh split on the different cost components.
in network peaks and also has the highest EB generation in low price hours. Finally, it provides the highest value of the electric boiler as variable operating costs are greatly reduced, but the income to the DSO is low because the demand charge is avoided. RTP cause moderate to high use of EB with the highest share occurring in low price hours. Some EB use occurs in network peaks with this tariff structure. It cause rather low DSO income in TRP scenario because tariffs is a function of electricity prices that can be negative in TRP scenario. The costs reductions for the DHP are good in both electricity price scenarios.
market only. EB in DHP may also participate in balancing and regulating markets, where price variations are higher. This may represent a significant opportunity as more VRE causes more imbalances and need for short notice balancing power. Apart from grid tariffs, the EB use in DHP depends on multiple parameters such as the boiler capacities, storage options, heat demand and fuel prices, and the numerical results will hence vary according to changes in these parameters. For example, assuming lower LPG prices would result in reduced electricity use, especially if electricity grid costs and taxes are high.
5. Discussion and conclusions
5.2. Conclusions and recommendations
5.1. Discussion
The provision of flexibility to the power system from DHPs with EB is analyzed for different electricity grid tariff structures using a mixed-integer cost minimization model. The results show that electricity ta a large extent may replace costly fuels in district heating production when electricity is abundant, and that the grid tariff design is important to determine the extent of this. Both a typical hydropower and thermal power dominated power price structure are considered in this study together with four different tariff structures. The share of heat generated from EB varies from 7% to 17% with a hydro price pattern and from 2% to 13% with a thermal power price pattern, dependent on the assumed grid tariff structure. The EB is used significantly more under time-varying tariffs than under time invariant tariffs such as flat rate tariffs and standard demand charges. The critical peak price scheme proposed in this study shows particular potential to increase flexible P2H use and improve the profitability of P2H solutions. When assuming a thermal power price pattern - having large short-term variations demand charges are found to be a barrier for flexible EB use. Instead, more flexible and economic use of the EB is promoted by tariff structures with a low charge in low electricity demand hours and a higher charge when electricity demand is high. This study show how the structure of electric grid tariffs significantly influences the short-run flexibility provided by district heating plants, and the overall system effects should hence be assessed and considered when tariffs are designed and approved. Adaption of novel tariff schemes are important to unleash the potential for flexible use of DHPs and in long-run increase the renewable energy share in the heating sector. Future studies addressing tariff structure impacts on other flexible consumers and different district heating
The opportunities for improved VRE integration thorough power-to-heat (P2H) strategies has been highlighted in several previous studies, like [1,10,31]. This study confirms the findings from previous studies that both the level and the short-term variation of the electricity cost are decisive factors for cost optimal operation of EBs in district heating systems. The novelty in the present study is the modeling grid tariff structures' impacts on DHP's operation and flexibility provision. The model simulations demonstrates how different tariff structures may reinforce or hamper the flexibility provision, and in general the results show that tariffs with time-varying elements cause more flexibility provision compared to standard flat rate tariffs or demand charges. It should be noted that some consumer protection groups do not favor time-varying tariffs due to complexity and possible negative consequences for low-income customers. These negative effects can be reduced by introducing time varying tariffs as a nonmandatory option for customers who believe these tariffs benefit them [18]. It should be noted that the model has a perfect foresight approach, while the real-life planning is affected by uncertainty regarding future electricity prices and heat load [25,32]. Hence, the model result would not perfectly reflect the real DHP operation, but rather how price signals change the incentives for fuel shifting. Uncertainty regarding future prices is likely of importance under a demand charge because the whole future billing period is relevant in the EB operation decisions. In addition, the present study assumes that the DHP purchases electricity in the day-ahead spot
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plants can improve the robustness of these findings. Also, similar system benefits may be found for other consumers such as electrolysis plants producing hydrogen or charging stations for electric cars with large-scale battery storage. Future work should also address how uncertainty in future heat demand and electricity prices affect DHP operation under different tariff structures. Acknowlegdement This study is funded by Energy Norway through the Flexelterm project (www.flexelterm.no), project no. 226260/E20, with cofunding from The Norwegian Research Council. The authors thank the editor and three anonymous reviewers for their helpful comments. Nomenclature
Indices i m t Decision cfmt csmt cemt pimt ximt yimt pmax m
boilers, months hours in month variables Fuel cost Start-up cost Electricity cost Heat generation Binary unit commitment variable (1 if online, 0 otherwise) Start-up variable (1 if started in period t, 0 otherwise) Endogenously decided max level of heat delivered from electric boilers
Parameters P max , P min Maximum and minimum generation capacity [MW] Lmt Heat load [MW] hi Boiler efficiency in % FPi Price of fuel to boiler iV/MWh] Cis Start-up cost [V/MW] EPmt Wholesale electricity price ECm Grid tariff energy charge of grid tariff [V/MWh] DCm Grid tariff Demand charge [V/MW] ET Electricity tax [V/MWh) TF Tariff factor for dynamic energy charge Abbreviations VRE Variable renewable energy P2H Power-to-heat DHP District heating plant EB Electric boiler HP Heat pump DSO District system operator SRMC Short-run marginal cost LRMC Long-run marginal cost LPG Liquid petroleum gas HRP Hydro region price (scenario) TRP Thermal region price (scenario) FT Flat rate tariff structure (scenario) DC Standard demand charge based tariff structure (scenario) CPP Critical peak pricing RTP Real-time pricing
9
References [1] Lund PD, Lindgren J, Mikkola J, Salpakari J. Review of energy system flexibility measures to enable high levels of variable renewable electricity. Renew Sustain Energy Rev 2015;45:785e807. [2] IEA. Nordic energy technology perspectives. 2013. [3] Blarke MB. Towards an intermittency-friendly energy system: comparing electric boilers and heat pumps in distributed cogeneration. Appl Energy 2012;91(1):349e65. [4] Lund H. Large-scale integration of wind power into different energy systems. Energy 2005;30(13):2402e12. [5] Meibom P, Kiviluoma J, Barth R, Brand H, Weber C, Larsen HV. Value of electric heat boilers and heat pumps for wind power integration. Wind Energy 2007;10(4):321e37. [6] Kiviluoma J, Meibom P. Influence of wind power, plug-in electric vehicles, and heat storages on power system investments. Energy 2010;35(3):1244e55. [7] Lund P. Large-scale urban renewable electricity schemes e integration and interfacing aspects. Energy Convers Manag 2012;63(0):162e72. [8] Borenstein S. The long-run efficiency of real-time electricity pricing. Energy J 2005:93e116. [9] Eurelectric. Network tariff structure for a smart energy system. 2013. [10] Ueckerdt F, Hirth L, Luderer G, Edenhofer O. System LCOE: What are the costs of variable renewables? Energy 2013;63:61e75. [11] Simshauser P. Distribution network prices and solar PV: resolving rate instability and wealth transfers through demand tariffs. Energy Econ 2016;54: 108e22. [12] Honkapuro S, Tuunanen J, Valtonen P, Partanen J. DSO tariff structures: development options from stakeholders' viewpoint. Int J Energy Sect Manag 2014;8(3):263e82. € L, Koreneff G, Kekkonen V. Network tariff structures in Smart Grid [13] Simila environment. Research report. Espoo: VTT Technical research Centre of Finland; 2011. [14] Bartusch C, Wallin F, Odlare M, Vassileva I, Wester L. Introducing a demandbased electricity distribution tariff in the residential sector: demand response and customer perception. Energy Policy 2011;39(9):5008e25. [15] Schreiber M, Wainstein ME, Hochloff P, Dargaville R. Flexible electricity tariffs: Power and energy price signals designed for a smarter grid. Energy 2015;93(Part 2):2568e81. € der L. Distributed generation and distri[16] Picciariello A, Reneses J, Frias P, So bution pricing: why do we need new tariff design methodologies? Electr Power Syst Res 2015;119(0):370e6. rez-Arriaga JI, Abbad JR, Gonza lez JP. Distribution [17] Rodríguez Ortega MP, Pe network tariffs: a closed question? Energy Policy 2008;36(5):1712e25. [18] Borenstein S. Effective and equitable adoption of opt-in residential dynamic electricity pricing. Rev Ind Organ 2012;42(2):127e60. [19] Joskow PL. Chapter 16 regulation of natural monopoly. In: Polinsky AM, Shavell S, editors. Handbook of law and economics. Elsevier; 2007. p. 1227e348. [20] Crew, M.A., C.S. Fernando, and P.R. Kleindorfer, The theory of peak-load pricing: a survey. J Regul Econ. 8(3): p. 215e248. [21] Ausgrid. Initial pricing proposal for the finiancial year ending June 2016. 2015. € H. Tariff scheme options for [22] Partanen J, Honkapuro S, Tuunanen J, Niemela distribution system operators. Lappeenranta University of Technology; 2012. [23] Herter K, Wayland S. Residential response to critical-peak pricing of electricity: California evidence. Energy 2010;35(4):1561e7. [24] Herter K, McAuliffe P, Rosenfeld A. An exploratory analysis of California residential customer response to critical peak pricing of electricity. Energy 2007;32(1):25e34. [25] Ottesen SO, Tomasgard A. A stochastic model for scheduling energy flexibility in buildings. Energy 2015;88:364e76. [26] Kelly D, Bruce A, Macgill I, Passey RJ. An assessment of the cost-reflectivity of proposed network tariffs in Australia. In: Asia pacific solar Research conference; 2015. [27] Sumbera J. Modelling generator constraints for the self-scheduling problem. Prague: University of Economics; 2012. [28] NordPoolSpot. 2012 [cited 2013; Available from: http://www.nordpoolspot. com/historical-market-data/. [29] Hafslund. Grid rental prices. 2016. Available from: https://www.hafslundnett. no/english/customer/grid_rental_prices_2016/15502. [30] Tookanlou MB, Ardehali MM, Nazari ME. Combined cooling, heating, and power system optimal pricing for electricity and natural gas using particle swarm optimization based on bi-level programming approach: Case study of Canadian energy sector. J Nat Gas Sci Eng 2015;23:417e30. [31] Müller S. The power of transformation - wind, sun and the economics of flexible power systems. In: IEA grid integration of variable renewables (GIVAR III) project. Internationational Energy Agency; 2014. [32] Nielsen MG, Morales JM, Zugno M, Pedersen TE, Madsen H. Economic valuation of heat pumps and electric boilers in the Danish energy system. Appl Energy 2016;167:189e200.
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Energy journal homepage: www.elsevier.com/locate/energy
Impacts of electricity grid tariffs on flexible use of electricity to heat generation Jon Gustav Kirkerud*, Erik Trømborg, Torjus Folsland Bolkesjø Norwegian University of Life Sciences, Department of Ecology and Natural Resource Management, Norway
a r t i c l e i n f o
a b s t r a c t
Article history: Received 1 December 2015 Received in revised form 13 June 2016 Accepted 18 June 2016 Available online xxx
District heating plants having both electric boilers and alternative fuel options could hold a key in providing flexibility needed for cost efficient integration of variable renewable power. The electricity grid tariff is an important component of the electricity costs of electric boilers, and these tariffs may promote or hamper flexible use of power-to-heat. In this paper, a mixed integer cost minimization model that schedules the operation of different boilers in a district heating plant is developed and applied to analyze the impact of different tariff structures on flexibility provided by electric boilers. The results confirm that the structure of electric grid tariffs significantly influences the flexibility provided and the annual shares of electric boiler use, caused by differences in grid tariff structures, vary from 2% to 17%. Novel tariff structures with time-varying elements increase utilization electricity in low price periods and improve the profitability of power-to-heat as a flexibility solution. The study clearly demonstrates that system effects should be considered when grid tariffs for flexible electric boilers are designed and that novel tariff designs should be more widely adapted. © 2016 Elsevier Ltd. All rights reserved.
Keywords: District heating Power-to-heat Variable renewable energy integration Mixed integer model Grid rent
1. Introduction New variable renewable energy (VRE) sources are increasing their share in worldwide electricity generation as a result of a need to decrease fossil-based power generation, while maintaining energy security. It is well known that high VRE shares cause challenges in load regulation, since the VRE supply cannot be regulated and storage of electricity has high costs. A recent review study [1] concludes that increased integration of thermal and electric systems (P2H) is promising for provision of flexibility needed for renewable power integration. District heating plants (DHP) with several fuel options can provide such flexibility if electricity is used for heating in periods with high power supply and low demand and other sources such as biomass is used when demand is high relative to supply. P2H in DHP has a large potential; for example in the Nordic region the DH generation is around 130 TWh, which correspond to about 30% of the size of the Nordic electricity market [2]. Electric boilers (EB) and heat pumps (HP) are mature P2H technologies available in the market. EB is in general more suited for flexibility purposes than HPs since the HPs have the economic
* Corresponding author. P.O. Box 5003, NO-1432 Ås, Norway. E-mail address: [email protected] (J.G. Kirkerud).
characteristics of a base load technology e high investment costs and low operational costs [3]. The benefits of using EB in DHP for VRE integration has been addressed in several previous studies [4] strongly recommends using electricity and heat market interaction for increased energy system flexibility [5] studies the consequences of introducing these technologies into central cities in the Nordic energy market and concludes that it benefits the integration of wind power and saves fuel costs for heat producers. Also, [6], concludes that electric boilers provide substantial flexibility, especially for VRE, and that HPs combined with heat storage is a good solution to integrate baseload. Cities or municipalities can use P2H strategies to increase their share of renewable energy, according to [7]. To fully exploit the flexibility potential from P2H, prices must be efficient and time varying [8]. The retail price of electricity relative to other fuels determine when and how the electric boiler is used in a DHP. This cost consists of three components: wholesale electricity price, transmission costs (grid rent) and taxes. Taxes are usually low for industrial customers [9]. Wholesale electricity costs is usually the largest part and is normally charged based on the hourly wholesale price of electricity. In competitive markets, the hourly wholesale price provides efficient price signals conveying the short-term marginal cost of electricity generation. Transmission cost is the second largest cost component of an EB and comprises
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according to [9] 20e50% of total electricity costs in European countries. An increase in VRE deployment can cause this cost to further increase as these sources are often located far from load centers [10]. District system operators (DSOs) cover allowed costs, determined by electricity market regulators, through grid tariffs. However, time variation of tariffs are often neglected, as tariffs must be carefully designed and consider the interest of the DSO, the consumers and economic efficiency. This conflict of interest partly cause substantial variations in the actual tariff structure between countries and between DSOs. Consequently, conditions for flexible use of P2H vary widely and is seldom optimal. The introduction of smart meters with real-time measurements, combined with the recent increase in deployment of variable renewables has actualized grid tariff designs that increase demandside flexibility. Real-time measurements allow for tariffs designs that are more sophisticated. High VRE shares cause high short-run volatility of electricity prices and distributed VRE reduce utilization of the grid for some customers [11]. Different options and suggestions for changes in tariff design, from different viewpoints, have been discussed in the literature. Arguing from a DSO perspective [12], promotes an arrangement where customers pay for a subscription to a certain amount of power. Such tariffs secure a predictable income for DSOs [13]. discuss and simulate the effects of tariff structures on end-customer benefits and find that time varying pricing will be most beneficial [14] analyzed empirical data of hourly-metered consumption by residential customers in Sweden on tariffs and found that better tariff design could shift consumption from high demand hours to low demand hours. Finally [15], studies tariffs through simulations of flexible households and argues for flexible tariffs that increase with the hourly withdrawal of power from the grid. This reduces simultaneous peaks in demand caused by low price hours. Several studies focus on tariff designs to reduce the individual consumer's maximum consumption rather than the network's maximum consumption. In this study it is assumed that the latter is a more important driver of network costs for large scale consumers such as district heating plants. Also, many previous studies analyze the response to tariffs by consumers with a low degree of flexibility such as residential and services sector, whereas this study analyze large and very flexible consumers such as DHPs that can fully replace electricity consumption on short notice at a low cost. This type of consumers could hold a key in handling variable supply from VRE. The objective of this study is to analyze how electricity grid tariff structures affect the use of electricity and hence the role of the heating sector as a flexibility provider. The study compare and evaluate alternative structures, representing a range of possible options, based on typical tariff design principles as well as the ability to enable flexible response of P2H to electricity prices. For this purpose, a new DHP mixed integer optimization model is developed. The model minimizes the operational costs and capture variations in electricity prices, start-up costs of different boilers in a heat only plant, as well as the characteristics of different grid tariffs.
Economic efficiency principles state that tariffs should give the right price signals for both consumers and DSOs so that the socio-economic surplus is maximized both in the short and long term. Tariffs should reflect each network user's contribution to network costs to achieve cost-causality. The equity principle means charging “each consumer the same amount for using the same good or service, independently of the electricity's use and of the customer's characteristics.” Consumer protection principles emphasize the need for transparency and stability in the tariff design method, and a simple and understandable tariff structure. These principles contravene each other and a reasonable compromise must hence be found. Typically, consumer protection principles has been used as an argument against more economic efficient tariffs [18]. A design with high degree of time-varying pricing, to satisfy economic efficiency principles, can be difficult to communicate and understand meaning that the consumer protection principles is challenged. One possible approach, presented in [18], is to have both a default tariff structure that favors consumer protection principles and an optional tariff structure that pursue economic efficiency principles. Flexible consumers or consumers with load patterns that avoid peak hours will benefit from the optional tariff, while other consumers benefit from the default. This study asserts the need to find tariff schemes that sustain good tariff principles while still allowing for flexible use of P2H, thus a tariff with high degree of efficiency is desirable. 2.2. Time varying tariffs The economics of tariff design is much discussed in the literature (e.g. Refs. [11,19,20]) The electrical transmission grid is a natural monopoly, as the capital costs (fixed costs) are high compared to the short-run marginal costs (SRMC) (variable costs), which are primarily costs to cover grid losses. Variable user charges should therefore be set low to ensure high grid utilization in hours where grid capacity is sufficient. However, the demand for transmission vary greatly over the course of a day and a year, and the grid must be dimensioned to meet expected peak demand. The long-run marginal costs (LRMC) of increasing transmission during peak situations include additional capital and operational costs of incremental capacity. The LRMC of increasing demand in off-peak situations is low in comparison as only SRMC of existing capacity id included. This gives a rationale for peak pricing which discriminate between consumption in off-peak and peak hours. In such a system, a low tariff - reflecting SRMC only e is given to consumers during off-peak hours, and a high price reflecting LRMC is given in peak hours. The design of the grid tariff is usually structured into three main components: Fixed access charge (V/period) Energy charge (V/kWh/period) Demand or capacity charge (V/kWpeak/period)
2. Grid tariff design 2.1. Principles for tariff design Picciariello [16] and Rodríguez Ortega [17] identify principles for tariff design, here summarized into three main groups: System sustainability principles state that tariffs should recover the allowed costs for the DSO. A tariff structure that secures a stable yearly income is usually preferred over one that vary greatly from year to year.
The fixed charge is the cost of access to the grid regardless of the consumption and covers the residual costs. The energy charge is a cost per kWh electricity consumed. At minimum, the energy charge should reflect the short-run marginal cost of transmission, i.e. the marginal cost of covering grid losses. To reflect time variation in loss factors and electricity prices, the charge may differentiate between seasons and peak/off-peak hours or be settled dynamically based on the electricity price. It can also be used to signal long term marginal costs through time-of-use or critical peak pricing structures [21].
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In the demand charge, also referred to as capacity charge, the cost per kW are calculated based on the maximum load level(s) during the billing period. They describe costs for grid well as these are to a high degree capacity related. Demand charges requires more advanced metering equipment and is therefore most common for larger customers. Some versions of this charge are based on a subscribed level decided by the customer [22] or even the fuse size. 2.3. Effects of different tariff designs A common tariff design for small consumers have typically consisted of an access charge and an energy charge, because advanced metering is required for demand charges. Known as flat rate tariffs, these designs have the advantage of simplicity, but lack peak pricing. Compared to peak pricing, a high flat rate tariff will disincentivize EB generation in off-peak hours and incentivize in high peak hours. Time-of-use differentiation or critical peak pricing (CPP) can add temporal granularity to the energy charge. In time-of-use tariffs, selected hours (e.g. 7am to 7pm on weekdays) have a higher tariff. CPP often builds on top of a time-of-use structure, but have an extra charge in a few critical peak hours per year (50e100) declared in advance by the DSO. Results from a CPP program that have been tested in California can be found in Refs. [23] and [24]. A real-time pricing (RTP) structure, where the energy charge is a function of the electricity price, has potential benefits. Electricity prices are most often high when the load level in the grid is high and thus reflect grid costs in a limited extent. Time-varying energy charges gives a predictable cost for DHP operators and it is easy to determine dynamic elements such as CPP or a link to power prices. One disadvantage is that grid costs translates better to capacity (kW) than energy (kWh) and hence demand charges might be better suited. A standard form of the demand charge, as used in [25], charges a fee on the highest measured demand level within a month combined with a fixed charge and an energy charge. This design is well suited when the consumer's individual peak correlates with the network peak. However, a DHP with different fuel options will try to avoid electricity use in the network peak because power prices tend to be high in high demand periods. Instead, a DHP should have highest electricity consumption in hours with low power prices and hence relatively low electricity demand. Under demand charges, the marginal cost of using electricity depends on the number of hours electricity use is profitable, leading to uncertainty and suboptimal use of EBs: A billing period with few off-peak hours with low prices leads to less EB use and therefore a high demand charge per energy unit. Inversely, in a billing period with many off-peak hours with low prices (e.g. caused by VRE), the demand charge will be allocated on many hours. In the high load hours in that billing period, the marginal demand charge in peak hours is zero and there is no economic incentive to reduce peak load. In this regard, the standard demand charge cannot be classified as economically efficient in a power system perspective. According to [26], designs similar to the described demand charge exhibit poor cost reflectiveness, but an improvement is to charge on the measured peak load within typical peak hours (such as in Ref. [14]). An even better alternative would be to charge only on the measured peak load within critical peak hours. A demand charge based CPP design is likely to give a more stable cost recovery for the DSO compared to CPP based on energy charges. In addition, the DSO can be allowed to declare critical peaks in more hours of the year as this will not likely increase costs for consumers.
3
3. Methods 3.1. Model description A mixed integer cost minimization model that schedules the operation of different boilers in a district heating plant for a full year is developed and applied, and the effects of different grid tariff on the use of an EB in a DHP are analyzed under different power price scenarios. Mixed integer linear programs are commonly used for unit commitment and scheduling problems in electricity system modeling, but e as shown in this study e they can also explain the DHP planning challenges. The model developed in this study minimizes one year of operational costs for a DHP plant considering fuel costs, start-up costs, electricity prices and grid tariffs. The optimization horizon is one year divided into 12 months, each with 728 h, which gives 8736 h for a full year. Perfect foresight is assumed within the optimization period. The typical unit commitment elements (Equations (1)e(8)) of the model are based on Sumbera [27]. Equations (9)e(11) are new in this study and treat the grid tariffs. In the following description the indices for month are excluded for readability. A simplistic flow chart of the model is shown in Fig. 1. The objective function (1) minimizes costs for fuel cft start-up cst and electricity cet
MIN
XT t¼1
f
ct þ cst þ cet
(1)
Heat generation pit from each boiler i and hour t is constrained by maximum boiler capacity (2) and heat load Lt must be met at all times by the generation from the boilers (3):
pit P max ; Lt
ci; ct
XI
p ; i¼1 it
(2)
ci; ct
(3)
Fuel costs are a function of the fuel price FPi heat generation and the boiler efficiency hi (4):
cft ¼
XI
FP i¼1 i
pit
hi
;
ci; ct
(4)
For the calculation of start-up costs, a binary on/off variable xit or each unit is defined in (5) and (6) together with feasible area of operation:
xit P min pit ;
ci; ct
(5)
pit xt P max ;
ci; ct
(6)
The value for the binary start-up variable yit given in (7) and is associated with start-up costs Cis . (8). For t ¼ 1 in (7) xit1 is replaced by the x value for the last hour xiT from last month.
xit xit1 yit ; cst ¼
XI
Csy ; i¼1 i it
ci; t > 1
(7)
ci; ct
(8)
The cost of electricity consists of four components (9). The cost of electricity bought on the spot market at market price EPmt electricity tax ETm, and the energy charge of the grid tariff are all given on a per MWh basis. The demand charge DC is calculated based on the highest hourly load during the optimization period pmax , which is an endogenous variable, defined in (10). In one tariff structure studied (CPP, explained below), t in Equation (10) is exchanged with a subset of t which only includes hours of network peak load.
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Fig. 1. Simplistic flow chart of the model.
cet ¼
pit
hi
ðEPt þ EC þ ETÞ þ
pmax
hi
3.3. Electricity price and grid tariff data
DC;
ct;
i ¼ electric boilers (9)
XI
p i¼1 it
pmax ;
ct; i ¼ electric boilers
(10)
In the dynamic energy component option (11) replaces (9). In (11) the energy component is a function of the electricity price and a tariff factor TF.
cet ¼
pit
hi
ðEPt ð1 þ TFÞ þ ETÞ þ
pmax
hi
DC;
ct;
i ¼ electric boilers (11)
3.2. Data and assumptions The modelled plant, with techno-economic data as described in Table 1, represents a typical small-scale DHP in Norway, having three boilers: a biomass baseload boiler burning woodchips, a peak load boiler burning LPG (liquid petrol gas), and an electric boiler. The assumed conversion efficiencies are the lower heating values for various fuels. Fuel prices include emission taxes. Minimum loading conditions is considered only for the wood chip boiler. The assumed annual heat consumption including distribution losses is 80 GWh and maximum load is 30 MW. The distribution of heat demand per hour originates from actual heat load data from 2012 collected from Hafslund Varme's grid in Oslo. These data incorporates heat demand primarily from households and services sector buildings.
The retail price of electricity consists of three components: wholesale electricity price, grid tariffs and electricity tax. The electricity tax is the smallest component amounting to 0.6 V/MWh (4.5 NOK/MWh) in the case study. The modelled DHP is assumed to respond to the hourly price variations of the day ahead wholesale market. Two different power price series are analyzed (Figs. 2 and 3), reflecting the observed prices in 2012 for the Oslo spot price region in Norway (NO1) as well as the Western Denmark price region (DK1) [28]. The power price in Oslo represents a typical price structure of a hydropower region while West Denmark represents one of a thermal power dominated region with substantial wind power as well. As expected, the Danish price exhibits more short term price variations, with relatively high peak prices during the mid-day (Fig. 3). Moreover, high wind power penetration causes additional price variability and sometimes also negative prices. The Oslo region has lower short-term power price volatility, but usually larger variations over seasons and years. As shown in Fig. 3, the electricity market spot price (excluding grid rent and taxes) exceeds for most hours the assumed SMRC (short-run marginal cost) of the biomass boiler, but it is lower than the SRMC of the LPG boiler. In Oslo during summer, the spot prices are lower than SRMC for the biomass boiler for much of the time e due to high run-of-river generation. In the following, the two price series is referred to as the HRP (hydro region price) and the TRP (Thermal region price). 3.4. Grid tariff structures analyzed This study considers two elements of the grid tariff: energy charges and demand charges. The access charge is disregarded, since it does not influence operation of the electric boiler. The
Table 1 Technical and economic assumptions for the modelled plant.a
Wood chip boiler LPG boiler Electric boiler a
Capacity PMax [MW]
Efficiency h
Fuel price FP [V/MWh]
Minimum load Pmin [MW]
Start-up cost Cs [kV]
15 15 15
85% 92% 98%
25 55 variable
3 0 0
375 0 0
The exchange rate used for converting from NOK (Norwegian Krone) to Euro is 7.48, the time weighted average exchange rate in 2012.
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5
Fig. 2. Assumed weekly average electricity spot prices and grid tariff rates. Grid tariff levels are collected from Hafslund nett [29](Oslo DSO). The demand charge is 14.7 V/MW in January, February and December, 6.3 V/MW in March and November, and 1.1 V/MW in summer months. The energy charge is 3.3 V/MWh from November through March and 2.0 V/ MWh in summer months.
Fig. 3. Average wholesale electricity prices compared to SRMC of fuel based boilers shown with hourly resolution over the week (V/MWh).
baseline energy and demand charge components of the grid tariff are shown in Fig. 2. These are charges used by the DSO in Oslo for high voltage commercial customers [29] (exchange rate: 1 V is 7.48 NOK). The charges are highest during the winter because high demand for electric heating in Norway cause system demand peaks and high marginal grid losses. Four different tariff structures are analyzed: i) A standard flat rate structure (FT), ii) a standard demand charge based structure (DC), iii) a demand charge based critical peak pricing structure (CPP), and iv) a dynamic energy charge structure related to the electricity price (RTP). Table 2 summarize the details of the analyzed grid tariff structures. This study emphasizes the effects of tariff structure changes, not changes in the overall grid tariff level. In the model simulations, the tariff structures are leveled to generate the same level of tariff income to the DSO for a customer with a load pattern similar to system load. The country consumption profiles for Norway and Denmark 2012 [28] are used for this purpose. It is assumed that the sum of individual peak loads is 25% higher than the system peak load to account for imperfect
correlation in peak demands. The flat rate tariff structure (FT) consists of the baseline energy charge (Fig. 2) plus 13.7 V/MWh in all hours to compensate for not having a demand charge. FT represent typical tariff structures for smaller consumers without hourly metering and serves as a baseline in this case study. The demand charge tariff structure (DC) consists of the baseline energy charge and the baseline demand charge. A fee is charged on the consumer's maximum load within the monthly billing period. Time of use within the month is insignificant and every hour can act as a calculation hour. Contrary, in the critical peak pricing tariff structure (CPP), only hours where the electricity system load is particularly high can act as a calculation hour. High system load is defined here as the 5% hours of the year with highest system electricity demand. Electricity consumption during other hours will not trigger the demand charge in this tariff structure. CPP has a yearly billing period for the demand charge with an associated higher charge, and also contains the baseline energy charge. The real-time pricing tariff structure (RTP) consists of an energy charge only, calculated as the function of a
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Table 2 Summary of the grid tariff structures analyzed. Tariff structure
Description
Energy charge
Demand charge
Demand charge calculation
FT
Flat rate tariff
None
None
DC
Baseline
Peak demand/utilized capacity per month
CPP
Standard demand charge Critical peak pricing
Baseline þ 13.7 V/ MWh Baseline Baseline
RTP
Real time pricing
Spot-price 46.4%
59.6 V/kW/ year None
Peak demand/utilized capacity per year in system peak hours (5% hours with highest load in 2012) None
tariff factor and the wholesale electricity price. The tariff factor is set to 46.4% to ensure level tariff structures. 4. Results 4.1. Annual heat generation in biomass, LPG and electric boiler for different tariff structures Fig. 4 shows annual heat generation share from each boiler and for each electricity price scenario and grid tariff structure. In all scenarios, the biomass boiler supplies at least 78% of total generation. The minimum load requirement for the biomass boiler imply that some energy (0%e1.6% of total yearly heat generation) is cooled off, i.e. wasted, in the summer when heat consumption is low. As expected, scenarios with high biomass generation have more heat cooled off. When the electric boiler generation increases, it replaces both biomass and LPG boiler generation. In both price scenarios, CPP cause the lowest share of biomass and LPG generation. The highest share of LPG generation occurs under the DC tariff structure and the highest share of biomass generation occurs under FT for hydro region and DC for thermal region. 4.2. Electric boiler generation pattern under different tariff structures Fig. 5aed displays the generation patterns of the EB under different tariff structures. The characteristics of the price profiles discussed in chapter 3.2 cause corresponding variations in EB generation patterns in the two price scenarios. In the HRP scenario, the EB generates most during summer months due to low
electricity prices in the summer. In the TRP scenario, more low price hours occurs during winter causing more EB generation in those periods. There is also a clear difference in the hourly pattern (Fig. 5c and d), with most EB use during daytime in the HRP scenario oppositely to the TRP scenario where most EB use occurs during nighttime. Different tariff structures cause significant differences to the generation patterns. Firstly, the demand charge tariff structure (DC) eliminate all electricity use during winter weeks for two reasons: the demand charge is high during winter (Fig. 2) and off-peak hours are not exempt of the demand charge. Even with negative prices during some winter weeks in the TRP scenario, the demand charge efficiently block EB use. All other tariff structures allows some winter EB generation with the CPP allowing most. A second observation is that energy charge based structures, FT in particular and to some extent RTP, cause low summer generation. For FT, this is a direct result of the imperfections of flat rate tariffs, which overprice consumption in low demand periods. The EB generation pattern variations over the hours of the day also display relevant features of the tariff structures. The DC and FT tariff structure greatly reduce nighttime generation in the TRP scenario due to their flat tariff structure. With the DC tariff structure, the ability for the EB to react to hourly power price variations is particularly high. A standard demand charge indifferent of the hour of consumption can be satisfactory when electricity prices have a clear seasonal variation, but little intra-day variations. However, with more wind power having high generation in some winter weeks, the inability of this charge to encourage flexible P2H becomes prominent. A standard energy charge structure also comes up short, as EB generation in off-peak hours are as expensive as in peak hours.
Fig. 4. Share of heat generation covered by each boiler in the hydro region price (HRP) and thermal region price (TRP) scenario. Grid tariff structures are defined in Table 2.
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Fig. 5. aed: Generation patterns of electric boilers over weeks (a and b) and over hours of day (c and d) for HRP scenario (a and c) and TRP scenario (b and d).
FT stimulates to relatively low use of EB in both electricity price scenarios with correspondingly low use in hours when the electricity price is low. As there is no charge on peak load consumption, some use occurs in hours with high system load. The tariff structure generates high income for the DSO, but moderate cost savings for the DHP. DC has a very different impact on EB use in the HRP and TRP scenario. DC cause high EB use in HRP scenario due to low cost in summer months with accordingly low income for the DSO. The price structure of the TRP scenario combined with the DC tariff structure cause the lowest EB of all scenarios and accordingly low DSO income. The income to the DSO is moderate in the HRP scenario as demand charges are kept to a minimum. The costs reductions for the DHP are high in the HRP scenario, but very low in the TRP scenario. CPP cause the highest EB use of all tariffs because demand charge is calculated from only 5% of hours and electricity is hence cheap in many hours. It is efficient in reducing generation
4.3. Impact of grid tariff structures on electric boiler use and operational costs Table 3 displays important output parameters when assessing the impact of tariff structure on EB use in a flexibility perspective. In a security of supply perspective, it is desirable to use less electricity in network peaks, defined in this study as the 5% hours of the year with highest load. If EB use causes more electricity generation by fossil power plants, it results in increased emissions. For flexibility purposes, it is advantageous with electricity use in low load hours, defined here as hours with spot prices below 20 V/MWh. The tariff structures are in addition evaluated on the revenues for the DSO and the economic benefit for the DHP [30]. DHP benefits are calculated as the difference in variable operating costs with or without the electric boiler installed. The average cost of electricity per unit allocated to the different cost components are shown in Fig. 6. The observations displays major differences in the EB use characteristics and economics:
Table 3 Result summary of the impact of the grid tariff strictures defined in Table 2.
Hydro region price scenario Total EB generation (MWh) - EB generation in network peaks (5% hours with highest load) - EB generation in low price hours (spot price < 20 V/MWh) DSO income (kV) Reduced DHP variable operating cost (kV) Thermal region price scenario Total EB generation (MWh) - EB generation in network peaks (5% hours with highest load) - EB generation in low price hours (spot price < 20 V/MWh) DSO income (kV) Reduced DHP variable operating cost (kV)
FT
DC
CPP
RTP
5539 373 2221 92.3 41.5
8363 e 3975 39.0 90.6
13,812 e 4201 33.7 176.5
8466 208 4061 90.1 78.6
4172 158 1837 70.9 55.1
1621 e 912 9.2 19.7
10,282 e 3459 30.5 151.2
5355 111 3204 38.1 100.9
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Fig. 6. Average annual electricity costs per MWh split on the different cost components.
in network peaks and also has the highest EB generation in low price hours. Finally, it provides the highest value of the electric boiler as variable operating costs are greatly reduced, but the income to the DSO is low because the demand charge is avoided. RTP cause moderate to high use of EB with the highest share occurring in low price hours. Some EB use occurs in network peaks with this tariff structure. It cause rather low DSO income in TRP scenario because tariffs is a function of electricity prices that can be negative in TRP scenario. The costs reductions for the DHP are good in both electricity price scenarios.
market only. EB in DHP may also participate in balancing and regulating markets, where price variations are higher. This may represent a significant opportunity as more VRE causes more imbalances and need for short notice balancing power. Apart from grid tariffs, the EB use in DHP depends on multiple parameters such as the boiler capacities, storage options, heat demand and fuel prices, and the numerical results will hence vary according to changes in these parameters. For example, assuming lower LPG prices would result in reduced electricity use, especially if electricity grid costs and taxes are high.
5. Discussion and conclusions
5.2. Conclusions and recommendations
5.1. Discussion
The provision of flexibility to the power system from DHPs with EB is analyzed for different electricity grid tariff structures using a mixed-integer cost minimization model. The results show that electricity ta a large extent may replace costly fuels in district heating production when electricity is abundant, and that the grid tariff design is important to determine the extent of this. Both a typical hydropower and thermal power dominated power price structure are considered in this study together with four different tariff structures. The share of heat generated from EB varies from 7% to 17% with a hydro price pattern and from 2% to 13% with a thermal power price pattern, dependent on the assumed grid tariff structure. The EB is used significantly more under time-varying tariffs than under time invariant tariffs such as flat rate tariffs and standard demand charges. The critical peak price scheme proposed in this study shows particular potential to increase flexible P2H use and improve the profitability of P2H solutions. When assuming a thermal power price pattern - having large short-term variations demand charges are found to be a barrier for flexible EB use. Instead, more flexible and economic use of the EB is promoted by tariff structures with a low charge in low electricity demand hours and a higher charge when electricity demand is high. This study show how the structure of electric grid tariffs significantly influences the short-run flexibility provided by district heating plants, and the overall system effects should hence be assessed and considered when tariffs are designed and approved. Adaption of novel tariff schemes are important to unleash the potential for flexible use of DHPs and in long-run increase the renewable energy share in the heating sector. Future studies addressing tariff structure impacts on other flexible consumers and different district heating
The opportunities for improved VRE integration thorough power-to-heat (P2H) strategies has been highlighted in several previous studies, like [1,10,31]. This study confirms the findings from previous studies that both the level and the short-term variation of the electricity cost are decisive factors for cost optimal operation of EBs in district heating systems. The novelty in the present study is the modeling grid tariff structures' impacts on DHP's operation and flexibility provision. The model simulations demonstrates how different tariff structures may reinforce or hamper the flexibility provision, and in general the results show that tariffs with time-varying elements cause more flexibility provision compared to standard flat rate tariffs or demand charges. It should be noted that some consumer protection groups do not favor time-varying tariffs due to complexity and possible negative consequences for low-income customers. These negative effects can be reduced by introducing time varying tariffs as a nonmandatory option for customers who believe these tariffs benefit them [18]. It should be noted that the model has a perfect foresight approach, while the real-life planning is affected by uncertainty regarding future electricity prices and heat load [25,32]. Hence, the model result would not perfectly reflect the real DHP operation, but rather how price signals change the incentives for fuel shifting. Uncertainty regarding future prices is likely of importance under a demand charge because the whole future billing period is relevant in the EB operation decisions. In addition, the present study assumes that the DHP purchases electricity in the day-ahead spot
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plants can improve the robustness of these findings. Also, similar system benefits may be found for other consumers such as electrolysis plants producing hydrogen or charging stations for electric cars with large-scale battery storage. Future work should also address how uncertainty in future heat demand and electricity prices affect DHP operation under different tariff structures. Acknowlegdement This study is funded by Energy Norway through the Flexelterm project (www.flexelterm.no), project no. 226260/E20, with cofunding from The Norwegian Research Council. The authors thank the editor and three anonymous reviewers for their helpful comments. Nomenclature
Indices i m t Decision cfmt csmt cemt pimt ximt yimt pmax m
boilers, months hours in month variables Fuel cost Start-up cost Electricity cost Heat generation Binary unit commitment variable (1 if online, 0 otherwise) Start-up variable (1 if started in period t, 0 otherwise) Endogenously decided max level of heat delivered from electric boilers
Parameters P max , P min Maximum and minimum generation capacity [MW] Lmt Heat load [MW] hi Boiler efficiency in % FPi Price of fuel to boiler iV/MWh] Cis Start-up cost [V/MW] EPmt Wholesale electricity price ECm Grid tariff energy charge of grid tariff [V/MWh] DCm Grid tariff Demand charge [V/MW] ET Electricity tax [V/MWh) TF Tariff factor for dynamic energy charge Abbreviations VRE Variable renewable energy P2H Power-to-heat DHP District heating plant EB Electric boiler HP Heat pump DSO District system operator SRMC Short-run marginal cost LRMC Long-run marginal cost LPG Liquid petroleum gas HRP Hydro region price (scenario) TRP Thermal region price (scenario) FT Flat rate tariff structure (scenario) DC Standard demand charge based tariff structure (scenario) CPP Critical peak pricing RTP Real-time pricing
9
References [1] Lund PD, Lindgren J, Mikkola J, Salpakari J. Review of energy system flexibility measures to enable high levels of variable renewable electricity. Renew Sustain Energy Rev 2015;45:785e807. [2] IEA. Nordic energy technology perspectives. 2013. [3] Blarke MB. Towards an intermittency-friendly energy system: comparing electric boilers and heat pumps in distributed cogeneration. Appl Energy 2012;91(1):349e65. [4] Lund H. Large-scale integration of wind power into different energy systems. Energy 2005;30(13):2402e12. [5] Meibom P, Kiviluoma J, Barth R, Brand H, Weber C, Larsen HV. Value of electric heat boilers and heat pumps for wind power integration. Wind Energy 2007;10(4):321e37. [6] Kiviluoma J, Meibom P. Influence of wind power, plug-in electric vehicles, and heat storages on power system investments. Energy 2010;35(3):1244e55. [7] Lund P. Large-scale urban renewable electricity schemes e integration and interfacing aspects. Energy Convers Manag 2012;63(0):162e72. [8] Borenstein S. The long-run efficiency of real-time electricity pricing. Energy J 2005:93e116. [9] Eurelectric. Network tariff structure for a smart energy system. 2013. [10] Ueckerdt F, Hirth L, Luderer G, Edenhofer O. System LCOE: What are the costs of variable renewables? Energy 2013;63:61e75. [11] Simshauser P. Distribution network prices and solar PV: resolving rate instability and wealth transfers through demand tariffs. Energy Econ 2016;54: 108e22. [12] Honkapuro S, Tuunanen J, Valtonen P, Partanen J. DSO tariff structures: development options from stakeholders' viewpoint. Int J Energy Sect Manag 2014;8(3):263e82. € L, Koreneff G, Kekkonen V. Network tariff structures in Smart Grid [13] Simila environment. Research report. Espoo: VTT Technical research Centre of Finland; 2011. [14] Bartusch C, Wallin F, Odlare M, Vassileva I, Wester L. Introducing a demandbased electricity distribution tariff in the residential sector: demand response and customer perception. Energy Policy 2011;39(9):5008e25. [15] Schreiber M, Wainstein ME, Hochloff P, Dargaville R. Flexible electricity tariffs: Power and energy price signals designed for a smarter grid. Energy 2015;93(Part 2):2568e81. € der L. Distributed generation and distri[16] Picciariello A, Reneses J, Frias P, So bution pricing: why do we need new tariff design methodologies? Electr Power Syst Res 2015;119(0):370e6. rez-Arriaga JI, Abbad JR, Gonza lez JP. Distribution [17] Rodríguez Ortega MP, Pe network tariffs: a closed question? Energy Policy 2008;36(5):1712e25. [18] Borenstein S. Effective and equitable adoption of opt-in residential dynamic electricity pricing. Rev Ind Organ 2012;42(2):127e60. [19] Joskow PL. Chapter 16 regulation of natural monopoly. In: Polinsky AM, Shavell S, editors. Handbook of law and economics. Elsevier; 2007. p. 1227e348. [20] Crew, M.A., C.S. Fernando, and P.R. Kleindorfer, The theory of peak-load pricing: a survey. J Regul Econ. 8(3): p. 215e248. [21] Ausgrid. Initial pricing proposal for the finiancial year ending June 2016. 2015. € H. Tariff scheme options for [22] Partanen J, Honkapuro S, Tuunanen J, Niemela distribution system operators. Lappeenranta University of Technology; 2012. [23] Herter K, Wayland S. Residential response to critical-peak pricing of electricity: California evidence. Energy 2010;35(4):1561e7. [24] Herter K, McAuliffe P, Rosenfeld A. An exploratory analysis of California residential customer response to critical peak pricing of electricity. Energy 2007;32(1):25e34. [25] Ottesen SO, Tomasgard A. A stochastic model for scheduling energy flexibility in buildings. Energy 2015;88:364e76. [26] Kelly D, Bruce A, Macgill I, Passey RJ. An assessment of the cost-reflectivity of proposed network tariffs in Australia. In: Asia pacific solar Research conference; 2015. [27] Sumbera J. Modelling generator constraints for the self-scheduling problem. Prague: University of Economics; 2012. [28] NordPoolSpot. 2012 [cited 2013; Available from: http://www.nordpoolspot. com/historical-market-data/. [29] Hafslund. Grid rental prices. 2016. Available from: https://www.hafslundnett. no/english/customer/grid_rental_prices_2016/15502. [30] Tookanlou MB, Ardehali MM, Nazari ME. Combined cooling, heating, and power system optimal pricing for electricity and natural gas using particle swarm optimization based on bi-level programming approach: Case study of Canadian energy sector. J Nat Gas Sci Eng 2015;23:417e30. [31] Müller S. The power of transformation - wind, sun and the economics of flexible power systems. In: IEA grid integration of variable renewables (GIVAR III) project. Internationational Energy Agency; 2014. [32] Nielsen MG, Morales JM, Zugno M, Pedersen TE, Madsen H. Economic valuation of heat pumps and electric boilers in the Danish energy system. Appl Energy 2016;167:189e200.
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