Optimal dispatch of combined heat and power units based on particle swarm optimization with genetic algorithm Open Access

The large-scale utilization of intermittent wind energy and solar energy has produced many challenges to the stable dispatching and operation of the power system. Besides, renewable energy cannot be fully utilized due to the difficulty in local consumption, which results in a large amount of energy loss.

Many research scholars have focused on the aspects of improving the theoretical prediction accuracy of wind and photovoltaic (PV) power generation^1–5 and the practical large-capacity energy storage technology in order to resolve the above problems.^6–8 However, the inherent randomness of wind and solar energies cannot be eliminated, and the large-capacity energy storage technology is still in the preliminary stage. Schmidt’s research on the characteristics of wind power generation and photovoltaic power generation shows that the changes in different wind farms are highly correlated, while the changes in wind power generation and photovoltaic power generation are complementary.⁹ In Refs. 10 and 11, the complementarities of wind and photovoltaic resources in different periods are analyzed. The work of Refs. 12 and 13 indicates that the combination of wind energy and photovoltaic energy is more effective than a single photovoltaic power generation system or a wind power generation system and can improve the reliability and predictability of power production.

Therefore, in order to improve the stability of the power grid, the complementary characteristics of energy can be used to combine it with conventional units. On the basis of considering the stability of power output and the total annual power generation, Li and Qiu constructed a multi-objective optimization model for an integrated hydropower–photovoltaic power generation system.¹⁴ Tan et al. developed a collaborative power dispatch system to obtain the most profits from a regional power system consisting of biomass, thermal, and pumped storage power.¹⁵ The majority of the above research studies focus on the combination of different types of power generation resources, while some research studies have analyzed the feasibility of renewable energy in micro-grid power systems. Bekele and Tadesse researched the feasibility of a small-scale hydro–wind power generation system for off-grid rural electrification in Ethiopia.¹⁶ Ma et al. focused on the feasibility of a stand-alone hybrid solar–wind–battery system.¹⁷ Ma et al. also proposed a joint scheduling model of photovoltaic and pumped storage based on the technology and economy.¹⁸ 

In Ref. 19, a detailed analysis of the economic feasibility, potential energy saving, and environmental protection benefits of wind power consumption is made in the Netherlands. Reference 20 proposed an adjustment strategy based on the wind and hydrogen integrated energy network to reduce the abandonment rate, using hydrogen and heat as the energy storage media, combining electricity, heat, and gas networks, and using the complementary characteristics of multiple energy sources to improve system flexibility and, thus, enhance the abandoned wind to absorb capacity. Reference 21 proposed to configure a heat storage device in a thermal power plant to reduce the degree of thermoelectric coupling and took into account the influencing factors of on-grid electricity prices. An optimized scheduling model was established in consideration of fuel costs and environmental costs to ensure economical system operation. Reference 22 proposed to reduce the output of backpressure combined heat and power (CHP) units to ensure the space of wind power on-grid during low-load periods. With the maximum wind power dissipation rate as the optimization goal, a CHP unit to participate in the peak regulation schedule was established. Finally, simulation examples verify its feasibility. Reference 23 proposed that heat pumps and electric boilers can effectively improve the flexibility of the power system. Based on a two-stage stochastic programming method, an economical dispatch model for heat pumps and electric boilers was established and its ability to absorb and consume wind was verified through simulation. Reference 24 proposed to use regenerative electric boilers as peak dispatching resources, aiming to reduce the forced output of CHP units. When peak regulation is difficult, trying to reduce peak load values and increase trough load values increases winter wind power penetration. The coordinated scheduling model of source load is based on adjusting the load. Reference 25 proposed the solution of heating by using an electric boiler. The input of electric boilers has relatively increased the total local electricity load, providing more space for the grid-connected wind power while avoiding the emission of polluting gases caused by coal combustion. Reference 26 summarized the matching problem of energy production and consumption at the level of a combined electricity–heating system. The optimization design methods of heat storage devices in different application scenarios are proposed, which improves the ability to optimize the configuration of the energy system over large time and space, and can effectively solve the problems of renewable energy consumption and peak regulation. Reference 27 proposed a wind power-regenerative electric heating and boiler heating system. Based on the characteristics of China’s power system and considering the uncertainty of wind power, an optimization model for wind power heating and dispatching was established. The results show that this scheme can effectively improve the wind power absorption rate. Reference 28 analyzed the mechanism of heat dissipation and abandonment in different heat storage locations and the influence of parameters such as heat storage power and heat storage capacity on the improvement of the wind power dissipation effect and provided guidance for the practical project of using wind power for heat dissipation. Reference 29 proposed a coexistence model of wind power, CHP units, and conventional units, including heat storage devices, CHP units, and electric boilers for coordinated heating of the abandoned wind, and analyzed the effect of abandoned wind.

In this paper, a power generation model is proposed with priority given to the consumption of renewable energies including wind power, photovoltaic, hydropower, and thermal power units. However, some fluctuations caused by wind power and photovoltaic will be suppressed in order to achieve energy complementarity by the water storage capacity of the hydropower station. Based on CHP units, the power system and thermal system are combined to improve the capacity of optimal allocation of resources in a broader space-time range considering the actual problem of heating in winter in the north of China. According to the traditional particle swarm optimization (PSO) model, the natural selection mechanism of the genetic algorithm (GA) is adopted for reference in order to improve the accuracy of global optimization, which brings the economic benefits contributed by multiple renewable energy generation sources and provides practical guidance for its reliable operation.

The present research is organized in the following sequence: The optimal dispatch model has been built and illustrated in Sec. II. The optimal dispatch algorithm is illustrated in Sec. III. Moreover, numerical examples and simulation result analysis are presented in Sec. IV. Finally, some conclusions and potential future work are provided in Sec. V.

The objective of the economic optimal dispatch model of the power system with multiple renewable energy sources is to minimize the total generation cost, which consists of the conventional thermal power unit cost and the CHP unit cost. The objective function of the wind–photovoltaic–hydrothermal power system optimal dispatch model can be expressed as follows since the investment cost and the operation cost of the wind turbine, photovoltaic power plant, and hydropower plant are not considered:

where F represents the total generation cost, F₁ represents the conventional thermal power unit cost, P_i represents the electrical output power of the i conventional thermal power unit, F₂ represents the cost of the CHP units, P_e.j represents the electrical output power of the j CHP units, and P_i.j represents the thermal output power of the j CHP units.

The generation cost of the conventional thermal power unit consists of the following two parts: operation cost and start–stop cost,

where f₁ is the operation cost of the conventional thermal power unit, f₂ is the startup and shutdown cost of the conventional thermal power unit, u_i is the operation status of the i conventional thermal power unit; 1 represents the operation, and 0 represents the shutdown,

where a_i, b_i, and c_i are the second coefficients of the operation cost of the i conventional thermal power unit, P_i.t is the output power of the i conventional thermal power unit at time t, u_i.t is the start and stop states of the i conventional thermal power unit at time t, 1 represents operation and 0 represents shutdown, S_i is the starting cost of the conventional thermal power units, and N is the number of conventional thermal power units.

In the optimal dispatch of the wind–photovoltaic–hydrothermal power system, only the CHP units undertake the heating task and it is necessary to keep the unit running. Therefore, the unit cost of cogeneration only includes the operation cost, and the unit operation cost is related to the electrical output and the thermal output of the unit, that is,

where a_i, b_i, and c_i are, respectively, the operation cost coefficients of the j CHP units; P_e.j.t and P_h.j.t are, respectively, the electrical output power and the thermal output power of the j CHP units at t time; C_v is the operation coefficient of the CHP units, which is usually 0.15; and N_e is the number of CHP units.

The output power of a wind turbine is related to the wind speed at the height of the wind turbine hub without considering the wake flow and energy loss, that is,

where P_w.k.t is the actual output power of the k wind turbine at time t, P_w.k.R is the rated output power of the k wind turbine, v_k.t is the actual wind speed of the k wind turbine at time t, and v_k,in, v_k.out, and v_k.R are the cut-in wind speed, cutout wind speed, and rated wind speed of the k wind turbine, respectively.

Nowadays, the popularity of wind power has been significantly improved, and it is expected to continue to increase in the recent future. However, wind power is difficult to predict in essence due to its volatility and randomness. In some regions, such as Germany, system operators believe that renewable energy has a higher priority as compared to other conventional power generation. Therefore, the wind power output participates in the scheduling according to the predicted power during the scheduling process,

where $P¯$_w.k.t and P_w.k.t represent the predicted power and the rated output power of the k wind turbine at time t, respectively.

The photovoltaic cell model is used for modeling and solving to facilitate the calculation of the model. In this model, it is considered that the photovoltaic cell is only affected by the light intensity and environmental temperature and other disturbing factors are ignored,

where P_p.m.t represents the electrical output power of the m-group photovoltaic cell at any time, $Pp.mR$ represents the maximum electric power of the m-group photovoltaic cell under standard conditions (1000 W/m², 25 °C), G_m,t represents the light intensity of the photovoltaic cell group m at time t, k_t represents the power temperature coefficient, T_m.t represents the temperature of the photovoltaic cell group m at time t, $kT$ represents the temperature under standard conditions, i.e., reference temperature, 25 °C, and G^R represents the light intensity under standard conditions (1000 W/m²).

In the scheduling process, solar energy and wind energy participate in the scheduling by predicting the power output to ensure the priority consumption of renewable energy,

where P_p.m.t, $P¯$_p.m.t, and $Pp.mR$ represent the actual electric output power, predicted power, and rated power of m photovoltaic cells at time t, respectively.

Generally, hydropower stations are used for flood control, retaining water, power generation, and other tasks. The water consumption of daily power generation is required to be arranged according to the requirements of the hydropower dispatching department. In this model, it is considered that no “wastewater” will occur in order to ensure the full utilization of renewable energy,

where Q_l.min represent the minimum daily water consumption of hydropower station l, Q_l.max represent the maximum daily water consumption of hydropower station l, Q_l.t represents the actual water consumption of hydropower station l at time t, P_s.l.min represent the minimum technical outputs of hydropower station l, P_s.l.max represent the maximum technical outputs of hydropower station l, P_s.l.t represents the actual output of hydropower station l at time t, a represents the hydropower conversion constant, normally 9.81; η_l represents the efficiency of hydropower station l, and H_l,t represents the head height of reservoir l at time t.

The system balance constraints of the combined optimal scheduling model include electric power balance constraints and thermal power balance constraints.

The electric power balance constraint of the joint system can be expressed as follows, considering that the net loss and network limitation are ignored:

where N_w represents the number of wind turbines and P_d.t represents the actual value of the system electrical load at time t.

where P_h.j.t represents the thermal output power of the j CHP units at time t and P_h.z.t represents the actual value of the system thermal load at time t.

The conventional thermal power units and CHP units can only operate within their respective output regulation range, and their respective output constraints can be expressed as follows:

where P_i.min represents the minimum power of the j conventional thermal power unit, P_i.max represents the maximum power of the j conventional thermal power unit, and P_e.j.min and P_e.j.max represent the minimum electric output power and the maximum electric output power of the j CHP units, respectively.

It is considered that the regulation characteristics of each unit are different, and its regulation performance is limited by its own ramp rate during operation,

where $Pidown$ and $Piup$ are the ramp rates of the i conventional thermal power unit up and down, respectively, and $Pe.jdown$$Pe.jup$ are the upward and downward ramp rates of the j CHP units, respectively.

In order to ensure the stable operation of the power system, rotating reserve capacity is used, which is considered as one of the necessary conditions for the normal operation of the system,

where P_i.max represent the maximum generating power of the i conventional thermal power unit, P_e.j.max represent the maximum electrical output power of the jth CHP units, P_s.l.max represent the maximum technical output of the l hydropower station, respectively, and k_d, k_w, and k_p represent the system load fluctuation coefficient, wind power fluctuation coefficient, and photovoltaic fluctuation coefficient with values of 10%, 15%, and 20%, respectively.

Based on swarm intelligence proposed by Kennedy and Eberhart in 1995, PSO is an evolutionary computing technology. It originated from the study of the behavior of bird predation and considered an optimization tool based on iteration.³⁰ Obviously, the pace of the later evolution becomes slow because the random particles tend to be the same grade in the process of optimization, and it is easy to fall into the local optimal solution.

The GA is a computational model that simulates the biological evolutionary process of natural selection and genetic mechanism of Darwin’s theory of biological evolution. It is a method of searching the optimal solution by simulating the natural evolutionary process. Its main characteristics are that it directly operates on structural objects and there are no restrictions on the derivative and function continuity; it has inherent implicit parallelism and better global optimization capabilities; and it adopts a probabilistic optimization method, which does not require certain rules, can automatically obtain and guide the optimized search space, and adaptively adjust the search direction. The genetic algorithm targets all individuals in a population and uses randomization techniques to guide an efficient search of encoded parameter space. Among them, selection, crossover, and mutation constitute the genetic operation of the genetic algorithm; the five elements of parameter coding, initial population setting, fitness function design, genetic operation design, and control parameter setting form the core content of the genetic algorithm.

Therefore, the merits and demerits of the two algorithms are complementary considering the combination of the natural selection mechanism of GA and PSO, and the particle swarm optimization algorithm based on the natural selection mechanism is obtained. Nowadays, hybrid PSO and GA have been widely applied in a variety of research fields, including path planning,^32,33 network design,^34,35 optimal distributed generation location,^36,37 etc. In Ref. 38, an economic scheduling model is proposed, which considers the charging and discharging probability distribution of new energy vehicles and the random distribution of wind energy, and uses particle swarm optimization to solve the model. In Ref. 39, a novel approach to the economic dispatch (ED) problem using a hybrid intelligent algorithm has been proposed. This may be a good way to facilitate wind power integration by properly distributing a greater heat load to the CHP units that have lower efficiency. In Ref. 40, a novel optimization algorithm based on Particle Swarm Optimization (PSO) is proposed for solving the non-convex non-linear economic dispatch (ED) problem in a system integrated with combined heat and power.

For every iteration of the improved algorithm, all particles are grouped according to the size of the fitness value. Moreover, the speed and position of the worst half of the particles are replaced by the speed and position of the best half of the particles in the particle swarm. In addition, the historical optimal value that each individual remembers is retained.

The specific process related to the improved PSO algorithm is defined as follows:

1. The velocity and position of each particle in the particle swarm are initialized randomly, that is, the velocity and position of the i particle in the d-dimensional search space are considered to be V_i = (v_i.1, v_i.2, …, v_i.d) and X_i = (x_i.1, x_i.2, …, x_i.d), respectively.

2. Evaluate the fitness of each particle, store the current position and fitness of each particle in the individual extremum p_best, P_i = (p_i.1, p_i.2, …, p_i.d) of each particle, and store the position and fitness of the individual with the best fitness in the global optimal solution g_best, P_g.

3. Update the speed and position of the particle as follows:

where w is the inertia weight factor, c₁ and c₂ are the learning factors and c₁, c₂> 0, and r₁ and r₁ are the evenly distributed random numbers between 0 and 1.

1. The fitness value of each particle is compared with the best position it has experienced, and if it is better, it is considered as the current best position.

2. Compare the current values of all p_bests and g_bests, and update g_best.

3. Rank the particle swarm according to the fitness value, replace the speed and position of the worst half with the speed and position of the best half of the particles in the swarm, and keep the p_best and g_best unchanged.

4. If the preset operation accuracy is obtained, the search stops and the result is the output. Otherwise, return to the third step to continue the search.

To make a clear expression, the flowchart of the proposed algorithm is shown in Fig. 1.

A 24-h daily scheduling model with an interval of 1 h is used in the example. The optimal dispatch of wind–photovoltaic–hydrothermal power systems is based on CHP units, and the priority is given to renewable energy, which consists of conventional thermal power units, CHP units, and hydropower stations with an installed capacity of 300 MW, as well as a large number of distributed wind turbines and photovoltaic cells. In another work,³¹ the parameters of the conventional thermal power units are detailed. Table I shows the parameters and values of other units.

The model is solved in summer and winter in order to verify the rationality of the model. In the north of China, the power load and heat load are considered as the typical load in a certain area. Moreover, wind power and photovoltaic outputs are calculated based on the predicted values of two seasons in a certain area in the north of China. The demand for heat load in summer is significantly increased as compared to that in winter, the wind power output in the two seasons is observed to be relatively stable, and the photovoltaic power generation output is observed to be large in the peak load period, which can offset a part of the peak load to some extent. The specific forecast values of the two seasons are given in Figs. 2 and 3, respectively.

Based on the above parameter settings, the costs in different seasons are calculated in the simulation and the results after iteration are plotted as shown in Fig. 4. We tend to draw preliminary conclusions that compared to the traditional method, the PSO–GA method proposed in this paper has achieved fast convergence while reducing consumption in different seasons.

Based on the natural selection mechanism, the parameters of the particle swarm optimization algorithm are defined as follows. The population size N is 200, the maximum number of iterations M is 100, the learning factors are c₁ and c₂, respectively, and the inertia weight w is 0.7. Table II shows the total cost of the typical daily power generation before and after optimization in summer and winter and the proportion of consumption saved under the optimization. The proportion of each energy resource in different typical daily power generation is shown in Figs. 5 and 6.

The total electrical power provided by the three conventional thermal power units is 5076 MW, and the total electric power provided by the four cogeneration units is 14 283.91 MW according to the simulation results of typical days in summer. By contrast, 66.43% and 22.37% of the electric power of the typical conventional fire motor units and cogeneration units are observed in winter, respectively, with a little change in the proportion.

However, the total generation consumption is greater as compared to that in summer because of the large increase in the typical daily heat demand in winter. Table III provides the optimal electric power dispatching results of each unit in 24 h periods. Table IV shows the optimal thermal power dispatching results. Items A1–A3 in Table III represents the three conventional thermal power units, respectively. Items B1–B4 in Tables III and IV represent the four cogeneration units, respectively.

A wind–photovoltaic–hydrothermal power joint scheduling model is constructed in this paper. Giving priority to the consumption of renewable energy and the minimum total operating cost of the system is the primary objective, and a cogeneration unit is added to the model considering the practical heating problem. In order to solve the optimization of typical days in different seasons, the improved particle swarm optimization algorithm is adopted as well. The following conclusions are drawn from the simulation results:

1. The conventional thermal power units and cogeneration units can avoid frequent output regulation and can show good complementary characteristics.

2. The natural selection mechanism of the genetic algorithm is combined with the particle swarm optimization algorithm in order to make the simulation results accurate, taking into consideration the condition that the traditional particle swarm optimization algorithm is easy to fall into the local optimal solution in the process of optimization iteration.

3. The strategy of the priority consumption of renewable energy can improve the capacity of the power grid to accept renewable energy; provide a reference for the coordinated operation of new energy such as wind, power, and other energy; and respond according to the requirements.

The principle of the annual power generation plan arrangement of thermal power units will change in the near future, adhere to “heat-load-based,” improve uncertainty model fitting for wind power and photovoltaics, and encourage thermal power units to participate in peak regulation during the heating period. The advantages of centralized energy conservation and environmental protection of combined heat and power are fully utilized, and the maximum heating capacity and comprehensive energy utilization efficiency of the power unit are fully exploited. The combined heat and power unit should coordinate the planning and network operation with the heating boiler. The combined heat and power unit bears the basic heat load, the peak shaving boiler bears the peak heat load, and the peak shaving boiler operation time is reasonably controlled.

C.C. made optimal dispatch, and P.H. set up an experimental platform and performed a physical simulation. S.D. proposed a wind–photovoltaic–hydrothermal power joint scheduling model and polished the manuscript.

This research work was supported by the National innovation and entrepreneurship training program for College Students, Grant No. 201711075009.

The authors declare no conflicts of interest.

The MATLAB simulation data used to support the findings of this study are available from the corresponding author upon request.