Operating Strategies for a GB Integrated Gas and Electricity Network Considering the Uncertainty in Wind Power Forecasts

In many power systems, in particular in Great Britain (GB), significant wind generation is anticipated and gas-fired generation will continue to play an important role. Gas-fired generating units act as a link between the gas and electricity networks. The variability of wind power is, therefore, transferred to the gas network by influencing the gas demand for electricity generation. Operation of a GB integrated gas and electricity network considering the uncertainty in wind power forecast was investigated using three operational planning methods: deterministic, two-stage stochastic programming, and multistage stochastic programming. These methods were benchmarked against a perfect foresight model which has no uncertainty associated with the wind power forecast. In all the methods, thermal generators were controlled through an integrated unit commitment and economic dispatch algorithm that used mixed integer programming. The nonlinear characteristics of the gas network, including the gas flow along pipes and the operation of compressors, were taken into account and the resultant nonlinear problem was solved using successive linear programming. The operational strategies determined by the stochastic programming methods showed reductions of the operational costs compared to the solution of the deterministic method by almost 1%. Also, using the stochastic programming methods to schedule the thermal units was shown to make a better use of pumped storage plants to mitigate the variability and uncertainty of the net demand.

Abstract-In many power systems, in particular in Great Britain (GB), significant wind generation is anticipated and gas-fired generation will continue to play an important role. Gas-fired generating units act as a link between the gas and electricity networks. The variability of wind power is, therefore, transferred to the gas network by influencing the gas demand for electricity generation. Operation of a GB integrated gas and electricity network considering the uncertainty in wind power forecast was investigated using three operational planning methods: deterministic, two-stage stochastic programming, and multistage stochastic programming. These methods were benchmarked against a perfect foresight model which has no uncertainty associated with the wind power forecast. In all the methods, thermal generators were controlled through an integrated unit commitment and economic dispatch algorithm that used mixed integer programming. The nonlinear characteristics of the gas network, including the gas flow along pipes and the operation of compressors, were taken into account and the resultant nonlinear problem was solved using successive linear programming. The operational strategies determined by the stochastic programming methods showed reductions of the operational costs compared to the solution of the deterministic method by almost 1%. Also, using the stochastic programming methods to schedule the thermal units was shown to make a better use of pumped storage plants to mitigate the variability and uncertainty of the net demand.
Index Terms-Integrated gas and electricity network, stochastic programming, wind power forecast uncertainty.
Reynolds number.
Gas withdrawal. Wind power.
Spot price.
Fuel cost of power generation.
Variable (nonfuel) cost of power generation.

Scenarios.
Average value of a variable.
Standard condition for gas.
Gas storage facility.
Power generator.
Gas node.
Gas pipe.
Gas terminal.
Transmission line.

Parameters
Cross-sectional area of a pipe m .
Diameter of a pipe (m).
The probability of a wind power forecast scenario (%).
Gas temperature .
Gas density, assuming standard conditions kg/m .
Friction factor in a pipe.
Volume of a pipe m .
Gas turbine fuel rate coefficient of a compressor (0.084 m MJ). Expected value of a function.
Maximum generation capacity of a unit (MW).
Minimum power generation of a unit (MW).
Cool-down time .
Maximum cold startup cost .
Percentage of wind generation contributing to spinning reserve requirements (%).
Minimum reserve requirement to support generators outages and forecast errors in electricity demand (MW).
Minimum uptime for thermal units .
Minimum downtime for thermal units .
Compressor pressure ratio.
Volumetric gas flow rate m s .
Linepack changes m s .
Gas linepack m . Stored energy in a pumped storage unit (MWh).

I. INTRODUCTION
A S THE fraction of wind power generation in a power system increases, it becomes important to take account of the wind variability and the uncertainty in the forecasts of wind power.
Several studies have examined the effect of uncertainty in wind power forecasts on unit commitment. Carpentier et al. [1] presented a stochastic decomposition method to deal with large-scale unit commitment. Wang et al. [2] presented a security-constrained unit commitment algorithm to take into account the intermittency and uncertainty of wind power generation. In [3], a particle swarm optimization technique was used to solve a stochastic cost model considering load and wind power uncertainties. Gonzalez et al. [4] formulated a two-stage stochastic programming model to optimize the combined operation of a wind farm and a pumped storage facility in a market environment with wind generation and electricity price uncertainties. Bouffard and Galiana [5] formulated a short-term forward electricity market-clearing model for nondispatchable and variable wind power generation sources. Tuohy et al. [6] examined the effects of uncertain wind and load on the unit commitment and dispatch of power systems with high levels of wind power generation. Methaprayoon et al. [7] developed an artificial neural network model to generate uncertain wind power forecasts. This model was integrated into unit commitment scheduling.
Given the strong linkage between gas and electricity networks in Great Britain (GB), the ability of the power system to meet the uncertain net demand is affected by performance of the gas network [8]- [10]. Although the storage capacity of the gas transmission network provides a buffer to compensate for demand variations to a degree, gas supply and pressure in the network need to be adjusted to cope with more extreme cases. Therefore, modeling the integrated network using stochastic programming allows improved unit scheduling decisions to be made.
An integrated model of gas and electricity networks was developed to take into account the uncertainty in wind power forecast and fuel availability to gas-fired generators. The uncertainty in the forecasts of electricity demand is significantly less than that of wind power; therefore, in this research, only the uncertainty of wind power forecasts are considered.

II. OPERATIONAL PLANNING METHODS TO ADDRESS UNCERTAINTY IN WIND POWER FORECASTS
The uncertainty in wind power forecast was addressed using three operational planning methods: deterministic (DM), two-stage stochastic programming (TSM), and multistage stochastic programming (MSM). These methods were benchmarked against a perfect foresight method (PFM) which has no uncertainty associated with the wind power forecast. The fundamental theories of stochastic programming are described within [11].
Deterministic Method (DM): In the deterministic method, the decision on the day-ahead unit commitment was made using a single point wind power forecast. In order to compensate for any deviation of the wind power outturn from the single point forecast, a predetermined level of spinning reserve was maintained. Then given the committed units, economic dispatch decisions were determined for possible outturns of wind power (forecast scenarios). The reason for using the wind power forecast scenarios in making economic dispatch decisions is to take into account different possibilities of wind power outturn when the expected cost of operating the system is calculated.

Two-Stage Stochastic Method (TSM):
In the two-stage stochastic programming method, probabilistic wind power forecast scenarios were used. In the first stage of decision making, a unit commitment decision was made for the whole operating horizon (day-ahead scheduling) considering different possibilities of wind power outturn. Then in the second stage, economic dispatch decisions were made for the possible outturns of wind power.
Multistage Stochastic Method (MSM): Inthemultistagestochastic programming method, probabilistic wind power forecast scenarios were used. The MSM allows for making multiple day-ahead unit commitment decisions. There is a day-ahead unit commitment decision for each forecast scenario. Nonanticipativity constraints ensure that the decisions for different forecast scenarios are the same for the period when the forecast scenarios have not branched out yet. Therefore, in the MSM for each wind power forecast scenario, a unit commitment and an economic dispatch decision were made. In practice, when the uncertainties associated with wind power forecast are gradually observed, the appropriate unit commitment and economic dispatch decisions, that have already been made, will be adjusted.
The main difference between the above methods is the way that unit commitment and economic dispatch decisions were made. Given a single wind power forecast and probabilistic wind power forecast scenarios, the decision-making process of a system operator, in the presence of the uncertainty in wind power, was modeled using different operational planning methods. The type of wind power forecast (single forecast and probabilistic forecast scenarios) used by the above operational planning methods, along with the form of unit commitment and economic dispatch solutions (single set of solution and multiple sets of solutions), are shown in Table I.

III. MODELING OF THE GB INTEGRATED GAS AND ELECTRICITY NETWORK
In this section, the modeling of the GB integrated gas and electricity network is presented. The modeling was implemented using the Fico Xpress Optimization suite. The structure used for the model is shown in Fig. 1. This structure consists of two separate parts: a mixed integer linear programming (MILP) model for the electricity network (including unit commitment, economic dispatch, and load flow) and a nonlinear programming (NLP) model for the gas network. The electricity network model is solved first using a branch and bound algorithm. The results are used to determine the gas demand for electricity generation for use within the gas model. The gas network problem is then solved using successive linear programming (SLP).
The solution of the gas network model is then checked to make sure there is no gas load shedding due to additional gas demand from gas-fired generators. In the case when gas load shedding does occur, a heuristic method is used to constrain the power output from the gas-fired generators, and the electricity and gas models are run repeatedly until a feasible solution is obtained. From the optimization perspective, the solution is not globally optimal, since the optimization problems for gas and electricity networks are not treated as one problem. However, the structure replicates the way that the GB gas and electricity networks are operated. In practice, operation of these networks are optimized separately with the gas network supplying gas to gas-fired plants until it is not feasible to do so. The mixed integer linear optimization problem of the electricity network was solved using a branch and bound algorithm. The nonlinear optimization problem of the gas network was solved using successive linear programming (SLP).

A. Objective Function
Equation (1) shows the expected operational cost of the electricity network which consists of fuel and variable costs of power generation, cost of unserved electricity, startup and shutdown costs of thermal generating units. Equation (2) shows the expected operational cost of the gas network which consists of cost of gas supply from terminals, costs of gas injection into and withdrawal from gas storage facilities, cost of gas provided by linepack, and cost of unserved gas.
The objective function is to minimize the summation of the expected costs of gas and electricity networks (3): (1) Superscript represents scenarios of the probabilistic wind power forecast.
B. Electricity Network 1) Power Balance Constraint: The power balance constraint requires that the total generation is equal to the total demand minus the load shed at each time step (4) 2) Power Generation: Electrical power generation is kept within the physical limits of the generating units (5) 3) Ramp Rate Constraints: Power generators cannot ramp up or ramp down instantaneously. Therefore, the following constraints were imposed within the model: 4) Power Transmission: The electricity network was modeled using a dc power flow [12], [13]. The power transmission along each line was constrained by defining a maximum transmission capacity (8)

5) Startup Cost:
The startup cost of a thermal generating unit depends on its downtime; this will vary from a maximum cold start value to a much smaller value when the generating unit is still relatively close to its operating temperature. A typical startup cost function for a thermal generating unit has an exponential form [14]. Because the time step in this study is discrete, the exponential startup cost was approximated by using the step-wisefunctionshownbyFig.2.
The startup cost of thermal generating units was modeled using (9), as follows [15]: (9) where are fixed cost coefficients derived from the stepwise form of the startup cost function. The discretized startup costs for thermal generating units are shown in Table II, and were assumed to be the same for different technologies and capacities.
6) Shutdown Cost: A constant shutdown cost of 1000 [16] was assumed for thermal generating units (10) to model the waste of fuel when a unit is brought offline [14].

7) Part-Load Efficiency:
The impact of part-load efficiency on the generation cost of thermal generating units was taken into account . For the sake of simplicity, the part-load efficiency was modeled using a linear approximation depicted in Fig. 3 [17].
It was assumed that efficiency of thermal generating units vary with their power output. Minimum and maximum efficiencies of different thermal generating units are shown in Table III. 8) Spinning Reserve: Spinning reserve is used to control the frequency and to maintain the balance between power demand and supply at all times. The amount of available spinning reserve is equal to the unused capacity of synchronized generators which can be dispatched immediately upon decision of the system operator. The minimum spinning reserve requirement varies in different systems. In conventional systems, the required amount of spinning reserve is usually equal to the capacity of the largest generator, or a certain percentage of the peak load.
When using a deterministic approach, a higher level of reserve is required to deal with uncertainties within the wind power forecast. The reserve requirement equation shown in (11) consists of two parts representing reserve requirement for generating unit outages and uncertainty in wind forecast: (11) [17] where (12) In the stochastic programming methods, the uncertainties of wind forecasts are taken into account implicitly through representative wind forecast scenarios. Therefore, the reserve requirement in the stochastic programming methods was considered only for generating units outages where . 9) Minimum Uptime and Downtime: When a thermal generatingunitisupordownitmustremainsoforminimum and periods, respectively. Minimum up/down constraints were implemented using [15] (13) Minimum up/down time as well as ramp up/down data for different thermal generating units are shown in Table IV. 10) Pumped Storage Plant: The dynamic behavior of pumped storage units was modeled by defining the storage level of equivalent electrical energy (15) and by the constraints upon pumped storage power generation (16) where is pumping efficiency, is pumping power, and is the length of time step which is one hour in this study.

C. Gas Network
The components of the gas network modeled were the pipelines, compressors, storage facilities, and gas terminals. More details about modeling of a gas network can be found in [18] and [19]. The balance of total gas supply and demand at each time step was satisfied (17) 1) Gas Flow in a Pipe: The gas flow rate within each pipe was determined by the pressure difference between upstream and downstream nodes (18) where subscripts up and down refer to the upstream and downstream nodes of pipe ,and is length of the pipe. The "Panhandle A" implementation of the friction factor for high pressure networks Pascal was used. 2) Gas Storage: The amount of gas stored in a storage facility at each time step was constrained using (19) where and are gas withdrawal and injection, and constrained through (20) and (21), respectively: 3) Gas Compressor: Compressors are used in the gas transmission network to boost network pressure and thus ensure gas delivery to each demand node. The power required by the compressor prime-mover is calculated by [18] (22) where superscripts in and out refer to the inlet and outlet of the compressor.
In practice, performance of a compressor is restricted by the pressure ratio (23), flow capacity (24), and maximum power (25): The amount of gas tapped by the compressor as fuel was approximated by [20] (26) 4) Gas Network Linepack: Linepack refers to the volume of gas stored within a pipe and is a key factor that affects the ability of a network to supply gas to demand nodes, i.e., a highly packed pipe allows fluctuations in demand to be met locally as gas supply from a distant source will take time (typically hours) to reach its intended destination.
The linepack of a pipe when the gas flow is in steady state is calculated using (27) This illustrates that pipe linepack is proportional to the average pressure within the pipe, so that an increase of average pressure will increase the linepack and vice versa.
The gas density and gas temperature under standard condition are 0.713 kg/m and 288 K. Under dynamic situations, the gas flow into and out of a pipe fluctuates with changing supply and demand. According to the law of conservation of mass, the change of total gas volume is equal to the difference between the flow into and out of the pipe. Thus, (27) is changed to (28) where the initial gas stored in the pipe is calculated by (27) in the steady state condition, and superscripts in and out refer to gas flows into and out of a pipe.

D. Linkage Between Gas and Electricity Networks
Gas turbine generators link the gas and electricity networks. For the gas network, a gas turbine was looked upon as a gas load. Its value depends on the power output of the gas turbine. In the electricity network, the gas turbine generator is a source. The relationship between the gas fuel flow and the real electrical power generated is expressed as (29) IV. CASE STUDY

A. Integrated Gas and Electricity Network
The simplified electricity and gas networks for GB, shown in Figs. 4 and 5, were modeled. The networks are linked together through gas-fired generators. Electricity and gas demand profile are shown in Figs. 6 and 7. The capacity of generating units at different locations are shown in Table V. The capacity of the power transmission lines are shown in Table VI.
The variable nonfuel operating cost and fuel cost for different technologies are shown in Table III. For thermal units, fuel cost data is based on their maximum efficiency.

B. Probabilistic Wind Power Forecasts
Different steps of producing probabilistic wind power forecasts are shown in Fig. 8. A single wind power forecast was calculated using the singular spectrum analysis (SSA) technique [24]. Given the forecast errors of the aggregated outputs of the wind farms [25], lower and upper limits were determined for each time step where the wind power outturn is most likely to fall within this range. Then a large number of random forecasts were generated within the lower and upper bounds using Monte Carlo simulation. It is worth noting that using the wider forecast error bounds improves the effectiveness of the stochastic programming methods.
It is very difficult to numerically obtain a solution for a stochastic optimization problem using the large number of wind power forecast scenarios [26]. On the other hand, a small number of wind power forecast scenarios provides less information about the possible wind power outturns. In order to address the above issues, a large number of wind power forecast scenarios were generated, and then a scenario reduction algorithm was applied to merge the forecast scenarios that are very close together. Fig. 9 shows the result of applying the scenario reduction algorithm [27] on the 1000 initial scenarios. The initial 1000 scenarios were reduced to 5 representative forecast scenarios showninFig. 10.
The stability of the scenario reduction algorithm was tested using a two-stage stochastic model for electricity network. The model was run several times with different numbers of forecast scenarios and then the operational costs were compared (Fig. 11).

A. Level of Spinning Reserve Used in the Deterministic Method (DM)
Dealing with the wind power uncertainty in the deterministic model necessitates the allocation of extra spinning reserve. Spinning reserve requirement for the single point wind power forecast (Fig. 10) for different values of [see (11)] are shown in Fig. 12. Impacts of applying different levels of spinning reserve on the operational cost of the electricity network are showninT ableVII.  In this research, 20% was considered to be an acceptable value for , due to providing reliable levels of reserve [28], [29] at reasonable operational costs. Therefore, results from the deterministic method with was compared to the results from the other methods.

B. Power Generation
Energy output from different types of generators for the perfect foresight method is shown in Fig. 13. Changes of electrical      methods, the nuclear power plants operate at their maximum capacity over the time horizon. This is due to the lower generation costs of these plants. In the deterministic method, the energy production from nuclear plants was slightly lower than the results from the other methods. Although, the nuclear plants are the cheapest option to meet the demand, more thermal generators came online in order to provide spinning reserve required.
In DM, the electrical energy produced by thermal generation units was less than the output from the same units in the other methods. This is because less energy was consumed by pumped storage plants to fill the reservoirs.
A number of committed thermal units are shown in Fig. 16. In the PFM, fewer units are committed since there is no need to provide reserve to compensate for the uncertainty associated with the wind power forecast.   Provision of spinning reserve capacity to compensate for the uncertainty of wind power forecast resulted in a larger number of committed thermal units in DM. Total electrical energy output, pumping energy, and level of storage for pumped storage plants in the perfect foresight method is shown in Fig. 15.
For the multistage stochastic programming method, there is a unit commitment solution for each forecast scenario (Fig. 17).

C. Gas Network Operation
The analysis of operation of the gas network showed that no load shedding occurred in any of the methods applied. However, in order to deal with the uncertainty of gas demand for power generation, in the deterministic method, higher gas pressure was maintained in the network to increase the linepack [see (27)] and make the network capable of meeting any deviation from the expected gas demand for power generation, locally. The higher pressure of the gas network is the result of the excessive operation of the compressors and has cost implications. The average linepack of the gas network and the total gas consumption by compressors are shown in Table VIII.  TABLE VIII  AVERAGE LINEPACK OF THE GAS NETWORK AND THE TOTAL GAS  CONSUMPTION

D. Operational Costs of the Integrated Network
The operational costs obtained from different methods are shown in Figs. 18 and 19, for the electricity network and the integrated network, respectively. Operational cost of the gas network contributed almost 60% of the total cost. In addition to the gas supplied to the gas-fired generators, 275 mcm gas was supplied to the nonpower sectors. The expected value of perfect information (EVPI) was approximated to be equal to 1million for DM. The value of the stochastic solution (VSS) for TSM and MSM are 0.7 million and 0.8 million pounds, respectively. The operational costs saving due to application of stochastic methods to schedule the GB gas and electricity network was calculated to be at least 255 million pounds in a year.
The computational times for each method are shown in Table IX. The experiments were executed on a laptop with i7-2640M CPU @ 2.80 GHz and 8 GB RAM. The mixed integer programming gap (MIP gap) of 0.8% was achieved in all the methods.

VI. CONCLUSION
Operation of the GB integrated gas and electricity network considering the uncertainty in wind power forecast was investigated using three operational planning methods: deterministic, two-stage stochastic programming, and multistage stochastic programming. These methods were benchmarked against a perfect foresight model which has no uncertainty associated with wind power forecast.
Comparison between the results obtained from different methods showed better performance of the integrated networks occurs when the stochastic programming methods were used. The use of the stochastic methods reduced the operational costs of the gas and electricity networks by almost 1%.
Gas supply constraints to the gas-fired generation units were taken into account through integrating a detailed gas network model to a unit commitment-electricity load flow model. The integrated gas and electricity network was also useful to analyze the impacts of wind forecast uncertainty on performance of the gas network.
The multistage stochastic programming, two-stage stochastic programming, and deterministic methods proposed the least expensive operational strategies for the integrated gas and electricity networks, respectively. The multistage stochastic programming method allows a system operator to improve the unit commitment and economic dispatch decisions at every time step given the constraints link the current state of the systems to the previous' and also take into account the remaining future uncertainties. This characteristic makes this method a useful approach for scheduling thermal generating units and operating the system in a day-ahead and intraday electricity markets.