CN111476394B - Robust operation optimization method suitable for multi-energy systems such as electric heating gas system - Google Patents
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Abstract
A robust operation optimization method suitable for an electric heating gas multi-energy system comprises the following steps: 1) the optimization model is based on a mixed integer linear programming formula, the formula is expanded on the basis, energy storage and heat storage are included, additional time-spanning constraint and operation uncertainty are included, an optimization target is as shown in a formula (1), and the expected energy consumption cost is the lowest; 2) the integrated network model is formulated by using an efficiency matrix representing the available multi-energy technologies as a means of coupling the power, thermal and gas network steady state models; 3) the iterative two-stage approach is based on piece-wise linear estimation of the loss and network limits. The invention realizes the optimized allocation of resources and improves the utilization efficiency of energy.
Description
Technical Field
The invention relates to a two-stage iterative method based on Mixed Integer Linear Programming (MILP) and nonlinear network equation linear approximation, which considers the constraints related to internal energy networks (such as electricity, heat and gas) and operation uncertainty (such as energy demand) and minimizes the total energy cost consumed in a multi-energy network.
Background
The energy is a power source for production and life, and is the basis for the survival and development of human society. Along with the rapid development of economic society, the energy consumption speed is rapidly increased, and environmental problems such as climate warming, air pollution and the like are increasingly intensified. Energy supply has become a key factor restricting sustainable development of human society, and controlling greenhouse gas emission and restraining climate warming has become a consensus of countries all over the world. The traditional energy system is limited to the inside of a system with a single energy form such as electricity, gas, heat (cold) and the like, and complementary advantages and synergistic benefits between the traditional energy system and the system cannot be fully exerted. For example, the power system lacks an energy storage device, and faces the difficulty and challenge of large-scale intermittent energy grid connection such as wind power and the like; and the stronger energy storage capacity of a natural gas system and a heating system is not exerted and utilized. Multiple energy sources are operated coordinately, advantages and potentials of different systems can be brought into play, renewable energy consumption ways are enriched, renewable energy consumption space is enlarged, and renewable energy consumption is promoted. Meanwhile, the overall planning of various energy sources considers that the resource optimal allocation can be realized in a wider range, and the energy utilization efficiency is improved.
The complexity of an intelligent multi-energy region is that it utilizes different energy carriers (e.g., electricity, heat, gas). Management of different energy carriers is achieved by Solid Oxide Fuel Cells (SOFCs), Electric Heat Pumps (EHPs), Electrical Energy Storage (EES), Thermal Energy Storage (TES), and Photovoltaic (PV) settings that combine power distribution, district heating, gas and other networks within a region. Integrated networks are becoming more important today as the increasing adoption of distributed technologies requires expensive network upgrades. It is more economically attractive to actively manage the integrated network with a partial flexibility of the smart cell. In order to properly simulate the actual operation of intelligent multi-energy source regions, including the impact on the integrated network, existing optimization and simulation tools must be improved. Existing optimization tools can model region operations based on uncertainty, cross-time constraints (e.g., related to storage), and different economic considerations. However, these tools tend to simplify areas by aggregating equipment at the building or regional level (e.g., using energy-centric approaches). In addition, these tools either ignore the complete network or rely on approximate simplified network equations. Therefore, these studies may provide infeasible solutions that may violate the technical limitations of the integrated network. Second, existing simulation models typically avoid infeasible network conditions by providing network parameters (e.g., losses) and stress conditions related to heat, pressure, voltage, and other techniques. However, these tools still rely on simplifications (e.g., snapshots, predefined storage usage, etc.) that do not adequately capture the complex combination of multi-stream interactions, uncertainties, and cross-time constraints.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a robust operation optimization method suitable for an electric heating gas multi-energy system, which adopts a two-stage iteration method based on Mixed Integer Linear Programming (MILP) and nonlinear network equation linear approximation, and optimizes the set values of all controllable devices (such as electricity and heat energy storage) in the MILP optimization stage by considering the uncertainty and linear approximation of an electricity, heat and gas integrated network; in the second stage, the accuracy of the linear model is improved by using a detailed nonlinear integration network model and by iteration between the models in the two stages.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a robust operation optimization method suitable for an electric heating gas multi-energy system comprises the following steps:
1) the optimization model is based on a mixed integer linear programming formula, the formula is expanded on the basis, energy storage and heat storage are included, additional time-spanning constraint and operation uncertainty are included, an optimization target is as shown in a formula (1), and the expected energy consumption cost is the lowest;
wherein, the first and the second end of the pipe are connected with each other,sis a time period; omegasIs the probability of occurrence of a scene/period s; pi Eis、πEosRespectively, the electric power import/export price (output) in s time period;
represents the input/output of the regional power in the s time period; pi Gis、
Respectively setting the price of the natural gas in the s time period and the input quantity of the regional natural gas in the s time period; b represents a building;
represent the costs of operation and maintenance of fuel cells, electric heat pumps, photovoltaics, gas boilers, energy storage and thermal energy storage, respectively, in the area;
output of heat energy for the gas boiler in s time; PF is a penalty function;
1.1) gas boiler model
The output heat of the gas boiler is a function of the gas input quantity and the efficiency, and as shown in the formula (2), the output heat of the gas boiler must be limited within the range shown in the formula (3);
wherein the content of the first and second substances,
in order to achieve the conversion efficiency of the gas boiler,
the gas input quantity of the gas boiler is;
1.2) Fuel cell model
The electrical and thermal output of the fuel cell are represented by (4) and (5), respectively, as linear functions of the gas input, and are expressed using a binary variable and two parameters. These linear equations may represent typical non-linear electrical and thermal efficiency functions given by the manufacturer, the power generation limit as equation (6), the ramp constraints (time dependent equation) as equation (7), and binary variables for the switchgear;
wherein, the first and the second end of the pipe are connected with each other,
for the binary variable of SOFC in s time, 0 or 1 can be taken;
as a function of the non-linear electrical and thermal efficiency of the SOFC;
is the charge and discharge rate limit of the SOFC in the region;
1.3) electric heating Pump model
The thermal output, power generation and ramp constraints for the electric heat pump model are (8), (9) and (10), respectively, as with the fuel cell, the ramp constraint is related to the capture time;
1.4) photovoltaic model
Wherein the content of the first and second substances,
efficiency of photovoltaic power generation in buildings;
photovoltaic power generation within s time;
the photovoltaic power generation reduction amount is reduced within s time;
1.5) energy storage model
Establishing time-varying energy output and input of the EES and the TES and SOC models as formulas (12) and (13), considering the SOC, limiting energy in equipment as (14) and (15), and constraining the slope of the stored energy charge-discharge rate as formulas (16) and (17);
wherein
The rise rate limits for energy storage cells and thermal energy storage in the zone, respectively;
1.6) energy balance
The energy balance is modeled on the building, network and regional level respectively, and at the building level, all surplus or deficit of power generation is balanced by the network, as shown in (18), (19) and (20);
wherein the content of the first and second substances,
respectively representing the electrical and thermal demands in the building over a time period s;
the input quantity of the natural gas in the s time period;
considering that a region may be composed of multiple networks, the energy may also be balanced at the network level, e.g. at connection points or substations, different electrical and thermal networks or network conditions within the region are modeled with (21) and (22);
wherein the content of the first and second substances,
the input of the power grid within s time;
the loss amount of the power grid in s time is obtained;
the loss of the heat supply network in s time is taken as the loss of the heat supply network;
at regional level, the net energy of the different networks is balanced by the upstream energy system, so only equations for power (23) and gas (24) balance are considered;
2) the integrated network model is formulated by using an efficiency matrix representing the available multi-energy technologies as a means of coupling the steady-state models of the electric, thermal and gas networks, which are solved in newton's method, if the network is integrated, coupling elements are included in the jacobian matrix, which are introduced by the multi-energy technologies, acting as relaxation generators, or providing active network management, so that if no coupling elements are present, the network is decoupled and can be solved accordingly; otherwise, modeling the power grid by using an integrated network model and using a typical active (25) and reactive (26) node balanced power flow equation;
modeling the thermal network based on node balances (27) and cumulative head losses (28);
wherein Cp is the specific heat capacity (4.182) of water (kJ/kg ℃);
the mass of the heat energy flow in the electricity, heat and gas nodes in s time; tsi,s，Tri,sIs s isTemperature of the thermal energy supplied and returned during the time; lhi,jIs the pipe length (hot); dhi,jTube diameter (hot); ρ g is the roughness of the pipeline;
modeling the gas network based on the node balance (29), the pressure drop (30) and the cumulative head loss (28);
wherein Fm2W is a conversion coefficient from flow to power; lgi,jIs the length of the trachea; dg, Dgi,jIs the diameter of the trachea; ρ g is the roughness of the pipeline;
3) the iterative two-stage method is based on piecewise linear estimation of loss and network limit, linear constraint firstly estimates the operation condition of the region through an optimization model, and then estimates the loss and the network limit through an integrated network model; next, distinguishing energy losses and network constraints based on electricity, heat and gas flow at the building level; if the heat inside the building is generated at different temperatures, losses and limitations must be distinguished according to each heating technique; as shown in (31), a difference constant (Kfd) is usednh,b,s、Kfdne,b,s、Kfdng,b,s) And independent constant (Kf)cs) To represent a linear approximation of the current violation of constraints and the loss estimated by optimization, this equation represents only one constraint, and also assuming that all devices produce heat at the same temperature, when additional constraints are introduced to create a piecewise approximation, the amount of loss does not include a penalty variable when modeling (xPF)S)；
Wherein BEN is a building connected with a regional power grid; xPFSA penalty variable for violating a network constraint; kfdnh,b,s、Kfdne,b,s、 Kfdng,b,sThe difference constants of the heating power, the electric power and the gas network in the area in s time are respectively;
these constraints do not force the optimizer to update the settings of the controllable devices, and the independent parameter (Kf) must be adjusted before the next iterationcs) And the solution is closer to the simulation condition.
Further, the step 3) adopts a thread cutting method, and comprises the following steps:
3.1) defining convergence criteria for the algorithm, the defined criteria including (i) a more accurate estimate of the loss, (ii) a reduction in the magnitude of violations, (iii) introducing new violations only if the maximum value of the new violations is below the constraint mean;
3.2) defining the baseline conditions based on violations and losses of network constraints, adjusting the independent parameter KfcsMatching the linear constraint with the simulation result of the comprehensive network, wherein the linear constraint is contained in the next optimization;
3.3) if the new set value meets all the convergence conditions, the model result is converged, and the previous steps are repeated. Otherwise, estimating new values for the independent parameters using linear interpolation between baseline and new data, adding a new constraint set to the optimization, and repeating this step;
3.4) if the optimized output matches the power loss and does not exceed the network limits, the set point is considered feasible.
The invention has the following beneficial effects: the resource optimal allocation is realized, and the energy utilization efficiency is improved.
Drawings
FIG. 1 is a flow chart of the coordinated optimization of electric heating gas multi-energy source area.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
Referring to fig. 1, a robust operation optimization method suitable for an electric heating gas multi-energy system includes the following steps:
1) the optimization model is based on a mixed integer linear programming formula, the formula is expanded on the basis, energy storage and heat storage are included, additional time-span constraint and operation uncertainty are included, an optimization target is shown as a formula (1), and the expected energy consumption cost is the lowest;
wherein, the first and the second end of the pipe are connected with each other,sis a time period; omegasIs the probability of occurrence of a scene/period s; pi Eis、πEosRespectively, the electric power import/export price (output) in s time period;
represents the input/output of the regional power in the s time period; pi Gis、
Respectively the natural gas price in the s time period and the regional natural gas input amount in the s time period; b represents a building;
the cost of operation and maintenance of fuel cells, electric heat pumps, photovoltaics, gas boilers, energy storage and thermal energy storage, respectively, in the area;
the output of the heat energy of the gas boiler is the region in s time; PF is a penalty function;
1.1) gas boiler model
The output heat of the gas boiler is a function of the gas input quantity and the efficiency, and as shown in the formula (2), the output heat of the gas boiler must be limited within the range shown in the formula (3);
wherein the content of the first and second substances,
in order to achieve the conversion efficiency of the gas boiler,
the gas input quantity of the gas boiler is;
1.2) Fuel cell model
The electrical and thermal output of the fuel cell are represented by (4) and (5), respectively, as linear functions of the gas input, and are expressed using a binary variable and two parameters. These linear equations may represent typical non-linear electrical and thermal efficiency functions given by the manufacturer, the power generation limit as in equation (6), the ramp constraint (time dependent equation) as in equation (7), and binary variables for the switchgear;
wherein the content of the first and second substances,
for the binary variable of SOFC in s time, 0 or 1 can be taken;
as a function of the non-linear electrical and thermal efficiency of the SOFC;
charge and discharge rate limitations for in-region SOFCs;
1.3) electric heating Pump model
The thermal output, power generation and ramp constraints for the electric heat pump model are (8), (9) and (10), respectively, as with the fuel cell, the ramp constraint is related to the capture time;
1.4) photovoltaic model
Wherein, the first and the second end of the pipe are connected with each other,
efficiency of photovoltaic power generation in buildings;
the photovoltaic power generation within s time;
the photovoltaic power generation reduction amount is reduced within s time;
1.5) energy storage model
Establishing time-varying energy output and input of the EES and the TES and SOC models as formulas (12) and (13), considering the SOC, limiting energy in equipment as (14) and (15), and constraining the slope of the stored energy charge-discharge rate as formulas (16) and (17);
wherein
The rise rate limits for energy storage cells and thermal energy storage in the zone, respectively;
1.6) energy balance
The energy balance is modeled on the building, network and regional level, respectively, and at the building level, all the surplus or deficit of power generation is balanced by the network, as shown in (18), (19) and (20);
wherein the content of the first and second substances,
respectively representing the electrical and thermal demand in the building over a period of s;
the input amount of natural gas in the s time period;
considering that a region may consist of multiple networks, the energy may also be balanced at the network level, for example at connection points or substations, different electrical and thermal networks or network conditions within the region being modeled with (21) and (22);
wherein the content of the first and second substances,
the input of the power grid within s time;
the loss amount of the power grid in s time is obtained;
the loss of the heat supply network in s time is shown;
at the regional level, the net energy of the different networks is balanced by the upstream energy system, so only equations for power (23) and gas (24) balance are considered;
2) the integrated network model is formulated by using an efficiency matrix representing available multi-energy technologies (e.g., EHP, CHP, etc.) as a means of coupling the steady-state models of the power, thermal, and gas networks, which are solved in newtonian terms, including coupling elements in the jacobian matrix if the network is integrated, the coupling elements being introduced by the multi-energy technologies, acting as relaxation generators, or providing active network management (e.g., pumps that control node pressures); thus, if no coupling element is present, the network is decoupled and can be solved accordingly; otherwise, using the integrated network model; the power grid is modeled by a typical active (25) and reactive (26) node balanced power flow equation;
modeling the thermal network based on node balances (27) and cumulative head losses (28);
wherein Cp is the specific heat capacity (4.182) of water (kJ/kg ℃);
the mass of the heat energy flow in the electricity, heat and gas nodes in s time; tsi,s，Tri,sFor supply in s time andthe temperature of the heat energy flowing back; lhi,jIs the pipe length (hot); dhi,jTube diameter (hot); ρ g is the roughness of the pipeline;
modeling the gas network based on the node balance (29), the pressure drop (30) and the cumulative head loss (28);
wherein Fm2W is a conversion coefficient from flow to power; lgi,jIs the length of the trachea; dgi,jIs the diameter of the trachea; ρ g is the roughness of the pipeline;
3) the iterative two-stage method is based on piecewise linear estimation of loss and network limit, linear constraint firstly estimates the operation condition of the region through an optimization model, and then estimates the loss and the network limit through an integrated network model; next, distinguishing energy losses and network constraints based on electricity, heat and gas flow at the building level; if the heat inside the building is generated at different temperatures, losses and limitations must be distinguished according to each heating technique; as shown in (31), a difference constant (Kfd) is usednh,b,s、Kfdne,b,s、Kfdng,b,s) And independent constant (Kf)cs) To represent a linear approximation of the current violation of constraints and the loss estimated by optimization, this equation represents only one constraint, and also assuming that all devices produce heat at the same temperature, when additional constraints are introduced to create a piecewise approximation, the amount of loss does not include a penalty variable when modeling (xPF)S)；
Wherein BEN is a building connected with a regional power grid; xPFSA penalty variable for violating a network constraint; kfdnh,b,s、Kfdne,b,s、Kfdng,b,sRespectively are the difference constants of the heat power, the electric power and the gas network in the area within s time; these constraints do not force the optimizer to update the settings of the controllable devices, and the independent parameter (Kf) must be adjusted before the next iterationcs) And the solution is closer to the simulation condition.
Further, the step 3) adopts a thread cutting method, and comprises the following steps:
3.1) defining convergence criteria for the algorithm, the defined criteria including (i) a more accurate estimate of the loss, (ii) a reduction in the magnitude of violations, (iii) introducing new violations only if the maximum value of the new violations is below the constraint mean;
3.2) adjusting the independent parameter (Kf) based on violations and losses of network constraints to define baseline conditionscs) Matching the linear constraint with the simulation result of the comprehensive network, wherein the linear constraint is contained in the next optimization;
3.3) if the new set value meets all the convergence conditions, the model result is converged, and the previous steps are repeated. Otherwise, estimating new values for the independent parameters using linear interpolation between the baseline and new data, adding the new constraint set to the optimization, and repeating this step;
3.4) if the optimized output matches the power loss and does not exceed the network limits, the set point is considered feasible.
Claims (2)
1. A robust operation optimization method suitable for an electric heating gas multi-energy system is characterized by comprising the following steps:
1) the optimization model is based on a mixed integer linear programming formula and comprises energy storage and heat storage, additional cross-time constraint and operation uncertainty, and an optimization target is as shown in a formula (1) and represents that the energy cost of expected consumption is the lowest;
wherein s is a time period; omegasFor scene/period sThe probability of birth; pi Eis、πEosRespectively, the electric power import/export prices in s time period;
represents input/output of regional power during the s period; pi Gis、
Respectively the natural gas price in the s time period and the regional natural gas input amount in the s time period; b represents a building;
represent the costs of operation and maintenance of fuel cells, electric heat pumps, photovoltaics, gas boilers, energy storage and thermal energy storage, respectively, in the area;
the output of the heat energy of the gas boiler is the region in s time; PF is a penalty function;
1.1) gas boiler model
The output heat of the gas boiler is a function of the gas input quantity and the efficiency, and as shown in the formula (2), the output heat of the gas boiler must be limited within the range shown in the formula (3);
wherein, the first and the second end of the pipe are connected with each other,
in order to achieve the conversion efficiency of the gas boiler,
the gas input quantity of the gas boiler is;
1.2) Fuel cell model
The electrical output and thermal output of the fuel cell are expressed as linear functions of the gas input by equations (4) and (5), respectively, and expressed by a binary variable for the switchgear and two parameters, the linear equations representing typical nonlinear electrical and thermal efficiency functions given by the manufacturer, the power generation limit as equation (6), and the ramp constraint as equation (7);
wherein, the first and the second end of the pipe are connected with each other,
taking 0 or 1 as a binary variable of the SOFC in the s time region;
as a function of the non-linear electrical and thermal efficiency of the SOFC;
is the charge and discharge rate limit of the SOFC in the region;
1.3) electric heating Pump model
The thermal output, power generation and ramp constraints for the electric heat pump model are respectively equation (8), equation (9) and equation (10), as with the fuel cell, the ramp constraint is related to the capture time;
1.4) photovoltaic model
Wherein the content of the first and second substances,
efficiency of photovoltaic power generation in buildings;
photovoltaic power generation within s time;
the photovoltaic power generation reduction amount is reduced within s time;
1.5) energy storage model
Establishing time-varying energy output and input of EES and TES and SOC models as formulas (12) and (13), considering energy limit in equipment as formulas (14) and (15) when SOC is considered, and constraining slopes of energy storage charge-discharge rate as formulas (16) and (17);
wherein
Rate of rise limits for energy storage cells and thermal energy storage in the zone, respectively;
1.6) energy balance
The energy balance is modeled on the building level, the network level and the area level respectively, and on the building level, all the surplus or deficit of power generation are balanced by the network, as shown in the formula (18), the formula (19) and the formula (20);
wherein the content of the first and second substances,
respectively representing the electrical and thermal demands in the building over a time period s;
the input quantity of the natural gas in the s time period;
considering that a region is composed of multiple networks, the energy is balanced between the networks, for example at the connection points or substations, the different electrical and thermal networks or network conditions within the region are modeled with (21) and (22);
wherein the content of the first and second substances,
the input of the power grid within s time;
the loss of the power grid within s time is obtained;
the loss of the heat supply network in s time is taken as the loss of the heat supply network;
at regional level, the net energy of the different networks is balanced by the upstream energy system, so only equations (23), (24) for power and gas balance are considered;
2) the integrated network model is formulated by using an efficiency matrix representing the available multi-energy technologies as a means of coupling the steady-state models of the electric, thermal and gas networks, which are solved in newton's method, if the network is integrated, coupling elements are included in the jacobian matrix, which are introduced by the multi-energy technologies, acting as relaxation generators, or providing active network management, if no coupling elements are present, the network is decoupled and solved accordingly; otherwise, modeling the power grid by using the integrated network model and using typical active and reactive node balanced power flow equations (25), (26);
modeling the thermal network based on node balancing (27) and cumulative head loss equations (28);
wherein Cp is the specific heat capacity of water;
the mass of the heat energy flow in the electricity, heat and gas nodes in s time; tsi,s，Tri,sThe temperature of the heat energy supplied and flowed back in s time; lhi,jIs the length of the pipeline; dhi,jIs the pipe diameter; ρ g is the roughness of the pipeline;
modeling the gas network based on node balancing (29), pressure drop (30) and cumulative head loss (28);
wherein Fm2W is a conversion coefficient from flow to power;
is the length of the trachea; dg, Dgi,jIs the diameter of the trachea; ρ g is the roughness of the pipeline;
3) the iterative two-stage method is based on piecewise linear estimation of loss and network limit, linear constraint firstly estimates the operation condition of the region through an optimization model, and then estimates the loss and the network limit through an integrated network model; next, distinguishing energy losses and network constraints based on electricity, heat and gas flow at the building level; if the heat inside the building is generated at different temperatures, losses and limitations must be distinguished according to each heating technique; as shown in equation (31), the disparity constant Kfd is usednh,b,s、Kfdne,b,s、Kfdng,b,sAnd independent constant KfcsTo represent a linear approximation of the current violation of the constraints and the loss estimated by optimization, this equation represents only one constraint, assuming all devices produce heat at the same temperature, and when additional constraints are introduced to create a piecewise approximation, the amount of loss does not include the penalty variable xPF when modelingS；
Wherein BEN is a building connected with a regional power grid; xPFSA penalty variable for violating a network constraint; kfdnh,b,s、Kfdne,b,s、Kfdng,b,sThe difference constants of the thermal, electrical and gas networks in the area in s time are respectively.
2. The robust operation optimization method for the electric heating gas multi-energy system according to claim 1, wherein the step 3) adopts a secant method, and comprises the following steps:
3.1) defining convergence criteria including (i) a more accurate estimate of the loss, (ii) reducing the magnitude of violations of the constraints, (iii) introducing new violations of the constraints only if the maximum value of the new violations of the constraints is below the constraint average;
3.2) defining the baseline conditions based on violations and losses of network constraints, adjusting the independent parameter KfcsMatching the linear constraint with the simulation result of the comprehensive network, wherein the linear constraint is included in the next optimization;
3.3) if the new set point meets all convergence conditions, the model results converge and the previous steps are repeated, otherwise, the new value of the independent parameter is estimated using linear interpolation between the baseline and the new data, a new constraint set is added to the optimization and the steps are repeated;
3.4) if the optimized output matches the power loss and does not exceed the network limits, the set point is considered feasible.
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